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best essays of analysis essay hills, 2007 ♥ home of fine hypertext products. I’ve had this damn thing up in a browser tab for literally months 1 and finally got around to reading it, “this damn thing” being editor David Foster Wallace’s introduction to The Best American Essays 2007. In it, Wallace describes his role in compiling the essays collection as that of The Decider. As in, he Deciders what goes into the book according to his subjective view and not necessarily because the essays are “Best”, “American”, or even “Essays”. Which, yes, all right, entitles you to ask what ‘value’ means here and whether it’s any kind of improvement, in specificity and sieve analysis, traction, over the cover’s ‘Best.’ I’m not sure that it’s finally better or less slippery than ‘Best,’ but I do know it’s different. ‘Value’ sidesteps some of the metaphysics that makes pure aesthetics such a headache, for analysis essay white one thing. It’s also more openly, candidly subjective: since things have value only to people, the idea of sieve, some limited, subjective human doing the valuing is sort of built right into the term. Analysis Essay Hills Like Elephants. That all seems tidy and all alone essay, uncontroversial so far although there’s still the question of just what this limited human actually means by ‘value’ as a criterion. Analysis Like White Elephants. One thing I’m sure it means is resume approved that this year’s BAE does not necessarily comprise the essay hills elephants, twenty-two very best-written or most beautiful essays published in lab report 2006. Some of the book’s essays are quite beautiful indeed, and most are extremely well written and/or show a masterly awareness of craft (whatever exactly that is).
But others aren’t, don’t, especially - but they have other virtues that make them valuable. And I know that many of these virtues have to do with the ways in which the pieces handle and respond to the tsunami of analysis essay elephants, available fact, context, and perspective that constitutes Total Noise. This claim might itself look slippery, because of course any published essay is when a formal essay a burst of information and context that is by definition part of 2007’s overall roar of info and analysis essay hills like, context. But it is possible for something to be both a quantum of information and a vector of meaning. Think, for instance, of the two distinct but related senses of ‘informative.’ Several of this year’s most valuable essays are informative in both senses; they are at once informational and instructive. That is, they serve as models and guides for how large or complex sets of facts can be sifted, culled, and arranged in meaningful ways - ways that yield and illuminate truth instead of just adding more noise to the overall roar. A Modest Essays. Although there are some differences between what Wallace and I consider valuable, the Decidering process detailed in his essay is a dead-on description of what I do on hills like white elephants, kottke.org every day. I guess you could say that it resonated with me as valuable, so much so that were I editing an resume approved end-of-the-year book comprised of the most interesting links from 2007, I would likely include it, right up front. Oh, and I got a kick out of the third footnote, combined here with the associated main text sentences: I am acting as an evaluative filter, winnowing a very large field of possibilities down to a manageable, absorbable Best for your delectation. Thinking about this kind of white elephants, Decidering is interesting in all kinds of different ways.
For example, from the perspective of Information Theory, the bulk of the Decider’s labor actually consists of excluding nominees from the final prize collection, which puts the Decider in exactly the position of three passions i have for essay, Maxwell’s Demon or any other kind of entropy-reducing info processor, since the really expensive, energy-intensive part of such processing is always deleting/discarding/resetting. My talk at hills elephants Ars Electronica 2006 on the topic of simplicity touched on similar themes and schoenberg new music essays by carl, the main point was that the more stuff I can sift through (and throw away), the better the end result can be. From this it follows that the more effective the analysis essay hills like, aggregator is at effectively determining what the group thinks, the better the end result will be. Schoenberg And The By Carl Dahlhaus. But somewhat paradoxically, the quality of the white elephants, end result can also improve as the complexity of the group increases. In constructing kottke.org, something that I hope is a simple, coherent aggregation of the world rushing past me, this complexity is my closest ally. Keeping up with so many diverse, independent, decentralized sources makes my job as an aggregator difficult reading 300 sites a day (plus all the other stuff) is no picnic but it makes kottke.org much better than it would be if I only schoenberg and the essays read Newsweek and watched Hitchcock movies. As artists, designers, and corporations race to analysis essay embrace simplicity, they might do well to schoenberg and the widen their purview and, in doing so, embrace the related complexity as well.
Welcome the chaos because there’s lots of good stuff to hills be found therein. I also attempted to tie the abundance of information (what Wallace refers to as “Total Noise”) and resume approved, the simplification process of editing/aggregating/blogging into analysis hills white elephants, Claude Shannon’s definition of information and information theory but failed due to time contraints and a lack of a modest proposal essays, imagination. It sounded good in analysis hills my head though. Anyway, if you’re wondering what I do all day, the answer is: throwing stuff out. kottke.org is not so much what’s on the site as what is not chosen for inclusion.  In actual fact, I closed that browser tab weeks ago and pasted the three i have lived for essay, URL into a “must-read items” text file I maintain.
But it’s been open in a browser tab in my mind for months, literally. That and I couldn’t resist putting a footnote in essay white elephants this entry, because, you know, DFW. #8617;
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Hills Like White Elephants - CliffsNotes
If correlation doesn’t imply causation, then what does? It is a commonplace of scientific discussion that correlation does not imply causation. Business Week recently ran an spoof article pointing out some amusing examples of the dangers of inferring causation from correlation. For example, the white elephants article points out all alone that Facebook’s growth has been strongly correlated with the yield on Greek government bonds: (credit) Despite this strong correlation, it would not be wise to conclude that the essay like success of resume approved Facebook has somehow caused the current (2009-2012) Greek debt crisis, nor that the Greek debt crisis has caused the adoption of Facebook!
Of course, while it’s all very well to analysis like white elephants piously state that correlation doesn’t imply causation, it does leave us with a conundrum: under what conditions, exactly, can we use experimental data to when a formal essay deduce a causal relationship between two or more variables? The standard scientific answer to like elephants this question is schoenberg and the essays dahlhaus that (with some caveats) we can infer causality from a well designed randomized controlled experiment. Unfortunately, while this answer is satisfying in analysis essay hills like white, principle and sometimes useful in practice, it’s often impractical or impossible to essays do a randomized controlled experiment. And so we’re left with the question of whether there are other procedures we can use to infer causality from experimental data. And, given that we can find more general procedures for inferring causal relationships, what does causality mean, anyway, for how we reason about a system?
It might seem that the answers to analysis essay hills white such fundamental questions would have been settled long ago. In fact, they turn out to analysis lab report be surprisingly subtle questions. Analysis Hills White. Over the past few decades, a group of scientists have developed a theory of causal inference intended to address these and resume approved other related questions. This theory can be thought of as an algebra or language for reasoning about cause and effect. Many elements of the theory have been laid out in a famous book by one of the main contributors to the theory, Judea Pearl. Although the theory of causal inference is not yet fully formed, and is still undergoing development, what has already been accomplished is interesting and worth understanding. In this post I will describe one small but important part of the essay like white theory of causal inference, a causal calculus developed by Pearl. Essay. This causal calculus is a set of three simple but powerful algebraic rules which can be used to essay like elephants make inferences about a night all alone, causal relationships.
In particular, I’ll explain how the causal calculus can sometimes (but not always!) be used to infer causation from a set of data, even when a randomized controlled experiment is not possible. Also in essay like white elephants, the post, I’ll describe some of the limits of the causal calculus, and some of my own speculations and questions. The post is a little technically detailed at new music essays dahlhaus points. Analysis Essay White Elephants. However, the first three sections of the post are non-technical, and a modest I hope will be of broad interest. Throughout the post I’ve included occasional “Problems for the author”, where I describe problems I’d like to solve, or things I’d like to understand better. Feel free to analysis essay like white elephants ignore these if you find them distracting, but I hope they’ll give you some sense of what I find interesting about the subject. Incidentally, I’m sure many of these problems have already been solved by others; I’m not claiming that these are all open research problems, although perhaps some are. They’re simply things I’d like to understand better. Also in the post I’ve included some exercises for the reader, and some slightly harder problems for when writing the reader.
You may find it informative to essay hills white elephants work through these exercises and problems. Before diving in, one final caveat: I am not an expert on causal inference, nor on statistics. Sieve Analysis. The reason I wrote this post was to help me internalize the ideas of the causal calculus. Occasionally, one finds a presentation of a technical subject which is hills elephants beautifully clear and illuminating, a presentation where the author has seen right through the subject, and is able to convey that crystalized understanding to others. That’s a great aspirational goal, but I don’t yet have that understanding of causal inference, and these notes don’t meet that standard. Nonetheless, I hope others will find my notes useful, and that experts will speak up to correct any errors or misapprehensions on my part. Let me start by explaining two example problems to illustrate some of the difficulties we run into when making inferences about causality. The first is known as Simpson’s paradox. To explain Simpson’s paradox I’ll use a concrete example based on all alone, the passage of the Civil Rights Act in the United States in 1964.
In the US House of Representatives, 61 percent of essay white Democrats voted for the Civil Rights Act, while a much higher percentage, 80 percent, of Republicans voted for the Act. You might think that we could conclude from this that being Republican, rather than Democrat, was an important factor in and the new music dahlhaus, causing someone to essay hills elephants vote for the Civil Rights Act. However, the picture changes if we include an additional factor in schoenberg and the dahlhaus, the analysis, namely, whether a legislator came from a Northern or Southern state. If we include that extra factor, the analysis essay white situation completely reverses, in both the essays North and the South. Here’s how it breaks down: North: Democrat (94 percent), Republican (85 percent)
South: Democrat (7 percent), Republican (0 percent) Yes, you read that right: in both the North and the South, a larger fraction of Democrats than Republicans voted for the Act, despite the elephants fact that overall a larger fraction of when essay Republicans than Democrats voted for the Act. You might wonder how this can possibly be true. Essay Hills White Elephants. I’ll quickly state the raw voting numbers, so you can check that the sieve arithmetic works out, and then I’ll explain why it’s true. You can skip the numbers if you trust my arithmetic. North: Democrat (145/154, 94 percent), Republican (138/162, 85 percent) South: Democrat (7/94, 7 percent), Republican (0/10, 0 percent)
Overall: Democrat (152/248, 61 percent), Republican (138/172, 80 percent) One way of understanding what’s going on is to note that a far greater proportion of analysis essay hills Democrat (as opposed to a modest proposal essays Republican) legislators were from the South. In fact, at the time the House had 94 Democrats, and only 10 Republicans. Because of analysis this enormous difference, the very low fraction (7 percent) of southern Democrats voting for the Act dragged down the Democrats’ overall percentage much more than did the even lower fraction (0 percent) of southern Republicans who voted for the Act. (The numbers above are for a night all alone the House of Congress.
The numbers were different in the Senate, but the same overall phenomenon occurred. I’ve taken the numbers from Wikipedia’s article about Simpson’s paradox, and there are more details there.) If we take a naive causal point of view, this result looks like a paradox. As I said above, the overall voting pattern seems to suggest that being Republican, rather than Democrat, was an important causal factor in voting for the Civil Rights Act. Yet if we look at the individual statistics in both the North and the South, then we’d come to the exact opposite conclusion. To state the analysis essay hills elephants same result more abstractly, Simpson’s paradox is the fact that the correlation between two variables can actually be reversed when additional factors are considered. So two variables which appear correlated can become anticorrelated when another factor is taken into all alone account. You might wonder if results like those we saw in voting on the Civil Rights Act are simply an unusual fluke. But, in fact, this is not that uncommon. Wikipedia’s page on Simpson’s paradox lists many important and similar real-world examples ranging from understanding whether there is gender-bias in university admissions to which treatment works best for hills elephants kidney stones. Three Passions Lived. In each case, understanding the causal relationships turns out to be much more complex than one might at first think.
I’ll now go through a second example of Simpson’s paradox, the kidney stone treatment example just mentioned, because it helps drive home just how bad our intuitions about statistics and causality are. Imagine you suffer from kidney stones, and your Doctor offers you two choices: treatment A or treatment B. Your Doctor tells you that the two treatments have been tested in a trial, and treatment A was effective for a higher percentage of patients than treatment B. If you’re like most people, at this point you’d say “Well, okay, I’ll go with treatment A”. Here’s the hills like white elephants gotcha. Keep in mind that this really happened . Suppose you divide patients in the trial up into writing a formal essay those with large kidney stones, and those with small kidney stones. Then even though treatment A was effective for a higher overall percentage of patients than treatment B, treatment B was effective for a higher percentage of patients in both groups , i.e., for both large and small kidney stones. So your Doctor could just as honestly have said “Well, you have large [or small] kidney stones, and treatment B worked for a higher percentage of patients with large [or small] kidney stones than treatment A”. If your Doctor had made either one of these statements, then if you’re like most people you’d have decided to go with treatment B, i.e., the exact opposite treatment.
The kidney stone example relies, of course, on the same kind of analysis hills like arithmetic as in the Civil Rights Act voting, and it’s worth stopping to resume approved figure out for essay hills like elephants yourself how the claims I made above could possibly be true. If you’re having trouble, you can click through to the Wikipedia page, which has all the details of the numbers. Now, I’ll confess that before learning about when writing a formal, Simpson’s paradox, I would have unhesitatingly done just as I suggested a naive person would. Indeed, even though I’ve now spent quite a bit of analysis essay hills like time pondering Simpson’s paradox, I’m not entirely sure I wouldn’t still sometimes make the same kind of mistake. I find it more than a little mind-bending that my heuristics about how to behave on the basis of statistical evidence are obviously not just a little wrong, but utterly, horribly wrong. Perhaps I’m alone in having terrible intuition about how to interpret statistics. But frankly I wouldn’t be surprised if most people share my confusion.
I often wonder how many people with real decision-making power – politicians, judges, and so on – are making decisions based on statistical studies, and yet they don’t understand even basic things like Simpson’s paradox. Or, to put it another way, they have not the first clue about statistics. Partial evidence may be worse than no evidence if it leads to an illusion of knowledge, and three i have so to overconfidence and certainty where none is justified. It’s better to analysis elephants know that you don’t know. Correlation, causation, smoking, and lung cancer. As a second example of the a night difficulties in establishing causality, consider the relationship between cigarette smoking and essay elephants lung cancer. In 1964 the United States’ Surgeon General issued a report claiming that cigarette smoking causes lung cancer. Three Lived. Unfortunately, according to hills elephants Pearl the evidence in the report was based primarily on correlations between cigarette smoking and writing essay lung cancer.
As a result the report came under attack not just by tobacco companies, but also by some of the world’s most prominent statisticians, including the great Ronald Fisher. They claimed that there could be a hidden factor – maybe some kind of genetic factor – which caused both lung cancer and essay white people to resume approved want to smoke (i.e., nicotine craving). If that was true, then while smoking and lung cancer would be correlated, the decision to smoke or not smoke would have no impact on whether you got lung cancer. Now, you might scoff at this notion. Hills White. But derision isn’t a principled argument. And, as the example of Simpson’s paradox showed, determining causality on the basis of correlations is tricky, at best, and can potentially lead to contradictory conclusions.
It’d be much better to have a principled way of using data to conclude that the relationship between smoking and lung cancer is not just a correlation, but rather that there truly is a causal relationship. One way of demonstrating this kind of causal connection is to do a randomized, controlled experiment. We suppose there is some experimenter who has the power to intervene with a person, literally forcing them to either smoke (or not) according to the whim of the experimenter. The experimenter takes a large group of people, and randomly divides them into two halves. One half are forced to smoke, while the a night other half are forced not to smoke. By doing this the experimenter can break the relationship between smoking and analysis hills like any hidden factor causing both smoking and essays dahlhaus lung cancer. By comparing the white elephants cancer rates in the group who were forced to schoenberg and the new music by carl smoke to those who were forced not to smoke, it would then be possible determine whether or not there is truly a causal connection between smoking and lung cancer.
This kind of randomized, controlled experiment is highly desirable when it can be done, but experimenters often don’t have this power. In the essay like elephants case of smoking, this kind of experiment would probably be illegal today, and, I suspect, even decades into the past. And even when it’s legal, in many cases it would be impractical, as in the case of the Civil Rights Act, and for many other important political, legal, medical, and resume approved econonomic questions. To help address problems like the two example problems just discussed, Pearl introduced a causal calculus. In the hills white remainder of this post, I will explain the rules of the sieve lab report causal calculus, and use them to analyse the analysis hills smoking-cancer connection. Sieve Analysis Lab Report. We’ll see that even without doing a randomized controlled experiment it’s possible (with the aid of some reasonable assumptions) to infer what the outcome of a randomized controlled experiment would have been, using only relatively easily accessible experimental data, data that doesn’t require experimental intervention to force people to smoke or not, but which can be obtained from purely observational studies. To state the rules of the causal calculus, we’ll need several background ideas. I’ll explain those ideas over the next three sections of this post. The ideas are causal models (covered in hills like white elephants, this section), causal conditional probabilities , and d-separation , respectively.
It’s a lot to swallow, but the ideas are powerful, and worth taking the time to understand. Passions I Have For Essay. With these notions under our belts, we’ll able to analysis essay hills like white understand the resume approved rules of the causal calculus. To understand causal models, consider the following graph of possible causal relationships between smoking, lung cancer, and some unknown hidden factor (say, a hidden genetic factor): This is a quite general model of causal relationships, in the sense that it includes both the suggestion of the US Surgeon General (smoking causes cancer) and also the suggestion of the tobacco companies (a hidden factor causes both smoking and cancer). Essay Like White. Indeed, it also allows a third possibility: that perhaps both smoking and three passions i have for essay some hidden factor contribute to lung cancer. Hills. This combined relationship could potentially be quite complex: it could be, for three passions lived for essay example, that smoking alone actually reduces the chance of lung cancer, but the hidden factor increases the chance of elephants lung cancer so much that someone who smokes would, on average, see an increased probability of lung cancer. This sounds unlikely, but later we’ll see some toy model data which has exactly this property. Of course, the model depicted in the graph above is not the most general possible model of causal relationships in this system; it’s easy to imagine much more complex causal models.
But at the very least this is an interesting causal model, since it encompasses both the US Surgeon General and the tobacco company suggestions. Essays. I’ll return later to the possibility of more general causal models, but for now we’ll simply keep this model in analysis essay hills white elephants, mind as a concrete example of a causal model. Mathematically speaking, what do the arrows of causality in the diagram above mean? We’ll develop an answer to that question over the next few paragraphs. It helps to start by analysis lab report moving away from the like elephants specific smoking-cancer model to writing essay allow a causal model to be based on a more general graph indicating possible causal relationships between a number of variables: Each vertex in this causal model has an associated random variable, . For example, in the causal model above could be a two-outcome random variable indicating the presence or absence of some gene that exerts an influence on hills like elephants, whether someone smokes or gets lung cancer, indicates “smokes” or “does not smoke”, and indicates “gets lung cancer” or “doesn’t get lung cancer”. The other variables and would refer to other potential dependencies in this (somewhat more complex) model of the smoking-cancer connection.
A notational convention that we’ll use often is to when writing a formal essay interchangeably use to refer to a random variable in the causal model, and also as a way of essay like labelling the corresponding vertex in the graph for the causal model. It should be clear from context which is meant. We’ll also sometimes refer interchangeably to the causal model or to essays the associated graph. For the notion of causality to make sense we need to constrain the class of graphs that can be used in a causal model. Obviously, it’d make no sense to analysis hills white elephants have loops in a modest, the graph: We can’t have causing causing causing ! At least, not without a time machine. Essay Like Elephants. Because of this we constrain the graph to be a directed acyclic graph, meaning a (directed) graph which has no loops in it. By the way, I must admit that I’m not a fan of the term directed acyclic graph. It sounds like a very complicated notion, at least to my ear, when what it means is very simple: a graph with no loops. For Essay. I’d really prefer to call it a “loop-free graph”, or something like that.
Unfortunately, the “directed acyclic graph” nomenclature is pretty standard, so we’ll go with it. Our picture so far is that a causal model consists of a directed acyclic graph, whose vertices are labelled by random variables . To complete our definition of causal models we need to capture the allowed relationships between those random variables. Intuitively, what causality means is that for any particular the only random variables which directly influence the essay like elephants value of resume approved are the parents of , i.e., the collection of random variables which are connected directly to . For instance, in essay hills like elephants, the graph shown below (which is the same as the complex graph we saw a little earlier), we have : Now, of course, vertices further back in the graph – say, the parents of the parents – could, of course, influence the value of . But it would be indirect, an influence mediated through the parent vertices. Note, by the way, that I’ve overloaded the notation, using to denote a collection of random variables. I’ll use this kind of schoenberg and the new music essays dahlhaus overloading quite a bit in the rest of analysis essay like elephants this post. In particular, I’ll often use the notation (or , or ) to denote a subset of lab report random variables from the graph. Motivated by the above discussion, one way we could define causal influence would be to require that be a function of its parents: where is some function. In fact, we’ll allow a slightly more general notion of causal influence, allowing to not just be a deterministic function of the parents, but a random function. We do this by requiring that be expressible in the form: where is a function, and is a collection of random variables such that: (a) the are independent of one another for different values of essay hills like white elephants ; and (b) for each , is independent of all variables , except when is itself, or a descendant of . The intuition is that the all alone essay are a collection of auxiliary random variables which inject some extra randomness into (and, through , its descendants), but which are otherwise independent of the variables in the causal model. Summing up, a causal model consists of a directed acyclic graph, , whose vertices are labelled by random variables, , and each is expressible in the form for some function . The are independent of one another, and each is analysis like elephants independent of all variables , except when is or a descendant of . In practice, we will not work directly with the resume approved functions or the auxiliary random variables . Analysis Like Elephants. Instead, we’ll work with the following equation, which specifies the causal model’s joint probability distribution as a product of conditional probabilities:
I won’t prove this equation, but the expression should be plausible, and and the new music essays by carl is pretty easy to prove; I’ve asked you to hills white elephants prove it as an optional exercise below. Prove the above equation for the joint probability distribution. (Simpson’s paradox in causal models) Consider the causal model of all alone essay smoking introduced above. Suppose that the essay hills like white hidden factor is a gene which is passions i have lived for essay either switched on or off. If on, it tends to make people both smoke and like white elephants get lung cancer.
Find explicit values for conditional probabilities in the causal model such that , and yet if the i have lived for essay additional genetic factor is taken into account this relationship is reversed. That is, we have both and . An alternate, equivalent approach to defining causal models is analysis like as follows: (1) all root vertices (i.e., vertices with no parents) in resume approved, the graph are labelled by independent random variables. (2) augment the essay white elephants graph by introducing new vertices corresponding to the . These new vertices have single outgoing edges, pointing to a night all alone essay . (3) Require that non-root vertices in the augmented graph be deterministic functions of their parents. The disadvantage of this definition is that it introduces the overhead of dealing with the augmented graph. But the definition also has the advantage of analysis essay hills like white cleanly separating the stochastic and deterministic components, and I wouldn’t be surprised if developing the theory of a night essay causal inference from this point of view was stimulating, at the very least, and may possibly have some advantages compared to the standard approach. Analysis. So the lab report problem I set myself (and anyone else who is interested!) is to carry the consequences of this change through the rest of the theory of causal inference, looking for advantages and disadvantages. I’ve been using terms like “causal influence” somewhat indiscriminately in the discussion above, and so I’d like to analysis like white elephants pause to discuss a bit more carefully about what is meant here, and schoenberg by carl what nomenclature we should use going forward. Analysis Essay Hills White Elephants. All the arrows in a causal model indicate are the possibility of a direct causal influence. This results in two caveats on proposal essays, how we think about causality in these models. First, it may be that a child random variable is actually completely independent of the value of one (or more) of essay white elephants its parent random variables.
This is, admittedly, a rather special case, but is perfectly consistent with the definition. For example, in a causal model like. it is possible that the outcome of cancer might be independent of the hidden causal factor or, for lab report that matter, that it might be independent of hills white elephants whether someone smokes or not. (Indeed, logically, at least, it may be independent of both, although of course that’s not what we’ll find in sieve analysis, the real world.) The second caveat in analysis hills like, how we think about the arrows and sieve causality is that the arrows only capture the direct causal influences in the model. It is possible that in a causal model like. will have a causal influence on through its influence on and . This would be an indirect causal influence, mediated by other random variables, but it would still be a causal influence. In the next section I’ll give a more formal definition of causal influence that can be used to make these ideas precise. In this section I’ll explain what I think is the most imaginative leap underlying the causal calculus. It’s the essay hills white introduction of the concept of causal conditional probabilities . The notion of ordinary conditional probabilities is no doubt familiar to you. It’s pretty straightforward to a night essay do experiments to estimate conditional probabilities such as , simply by looking at the population of people who smoke, and figuring out what fraction of those people develop cancer. Unfortunately, for the purpose of understanding the causal relationship between smoking and white elephants cancer, isn’t the quantity we want. As the tobacco companies pointed out, there might well be a hidden genetic factor that makes it very likely that you’ll see cancer in anyone who smokes, but that wouldn’t therefore mean that smoking causes cancer.
As we discussed earlier, what you’d really like to do in this circumstance is a randomized controlled experiment in which it’s possible for the experimenter to a night essay force someone to smoke (or not smoke), breaking the causal connection between the hidden factor and smoking. In such an experiment you really could see if there was a causal influence by looking at what fraction of people who smoked got cancer. In particular, if that fraction was higher than in the overall population then you’d be justified in concluding that smoking helped cause cancer. In practice, it’s probably not practical to do this kind of randomized controlled experiment. But Pearl had what turns out to be a very clever idea: to imagine a hypothetical world in which it really is possible to force someone to (for example) smoke, or not smoke. In particular, he introduced a conditional causal probability , which is the conditional probability of cancer in this hypothetical world. This should be read as the (causal conditional) probability of analysis hills like white elephants cancer given that we “do” smoking, i.e., someone has been forced to smoke in a (hypothetical) randomized experiment. Now, at first sight this appears a rather useless thing to do. But what makes it a clever imaginative leap is that although it may be impossible or impractical to do a controlled experiment to determine , Pearl was able to establish a set of rules – a causal calculus – that such causal conditional probabilities should obey.
And, by making use of this causal calculus, it turns out to sometimes be possible to infer the value of probabilities such as , even when a controlled, randomized experiment is impossible. And that’s a very remarkable thing to be able to do, and why I say it was so clever to have introduced the notion of causal conditional probabilities. We’ll discuss the resume approved rules of the causal calculus later in essay white elephants, this post. For now, though, let’s develop the essays notion of causal conditional probabilities. Essay Elephants. Suppose we have a causal model of some phenomenon: Now suppose we introduce an external experimenter who is able to intervene to deliberately set the value of a particular variable to . In other words, the experimenter can override the when writing a formal essay other causal influences on analysis elephants, that variable. This is equivalent to having a new causal model: In this new causal model, we’ve represented the experimenter by writing a formal a new vertex, which has as a child the vertex . All other parents of are cut off, i.e., the edges from the parents to are deleted from the graph. In this case that means the edge from to has been deleted. Analysis Essay White. This represents the passions lived for essay fact that the experimenter’s intervention overrides the other causal influences. (Note that the edges to the children of are left undisturbed.) In fact, it’s even simpler (and equivalent) to analysis essay consider a causal model where the lab report parents have been cut off from , and no extra vertex added: This model has no vertex explicitly representing the analysis experimenter, but rather the relation is replaced by passions for essay the relation . We will denote this graph by , indicating the graph in which all edges pointing to have been deleted.
We will call this a perturbed graph , and the corresponding causal model a perturbed causal model . In the perturbed causal model the only change is to delete the edges to , and to replace the relation by essay white elephants the relation . Our aim is to resume approved use this perturbed causal model to compute the conditional causal probability . In this expression, indicates that the term is omitted before the analysis like , since the value of is set on the right. By definition, the resume approved causal conditional probability is just the value of the probability distribution in the perturbed causal model, . To compute the value of the probability in the perturbed causal model, note that the analysis essay hills white probability distribution in the original causal model was given by. where the product on the right is over all vertices in the causal model. All Alone Essay. This expression remains true for the perturbed causal model, but a single term on the right-hand side changes: the conditional probability for the term. In particular, this term gets changed from to , since we have fixed the value of to be . As a result we have: This equation is a fundamental expression, capturing what it means for an experimenter to intervene to set the value of some particular variable in essay, a causal model. It can easily be generalized to a situation where we partition the variables into a night two sets, and , where are the variables we suppose have been set by intervention in a (possibly hypothetical) randomized controlled experiment, and are the analysis hills remaining variables:
Note that on sieve, the right-hand side the values for are assumed to analysis elephants be given by the appropriate values from and resume approved . The expression  can be viewed as a definition of causal conditional probabilities. Hills White. But although this expression is fundamental to a night all alone understanding the hills like elephants causal calculus, it is not always useful in practice. The problem is that the values of some of the variables on the right-hand side may not be known, and cannot be determined by experiment. Consider, for example, the case of smoking and cancer. Recall our causal model: What we’d like is to compute . Unfortunately, we immediately run into a problem if we try to use the expression on the right of equation : we’ve got no way of estimating the conditional probabilities for smoking given the schoenberg and the new music essays by carl dahlhaus hidden common factor. So we can’t obviously compute . And, as you can perhaps imagine, this is the kind of problem that will come up a lot whenever we’re worried about the possible influence of some hidden factor. All is not lost, however. Just because we can’t compute the expression on essay elephants, the right of  directly doesn’t mean we can’t compute causal conditional probabilities in other ways, and we’ll see below how the causal calculus can help solve this kind of problem. It’s not a complete solution – we shall see that it doesn’t always make it possible to compute causal conditional probabilities. But it does help.
In particular, we’ll see that although it’s not possible to a formal compute for this causal model, it is possible to compute in a very similar causal model, one that still has a hidden factor. With causal conditional probabilities defined, we’re now in position to define more precisely what we mean by causal influence. Hills Like. Suppose we have a causal model, and and are distinct random variables (or disjoint subsets of random variables). Essays By Carl. Then we say has a causal influence over if there are values and analysis like white elephants of and of such that . In other words, an external experimenter who can intervene to change the value of can cause a corresponding change in the distribution of values at . I Have For Essay. The following exercise gives an information-theoretic justification for this definition of causal influence: it shows that an experimenter who can intervene to analysis hills like white elephants set can transmit information to if and analysis lab report only if the above condition for causal inference is met. (The causal capacity) This exercise is for people with some background in information theory.
Suppose we define the causal capacity between and to be , where is the mutual information, the maximization is over like, possible distributions for (we use the hat to indicate that the value of is being set by intervention), and is the a night corresponding random variable at , with distribution . Analysis Essay Hills Like Elephants. Shannon’s noisy channel coding theorem tells us that an proposal, external experimenter who can intervene to set the value of can transmit information to an observer at at a maximal rate set by the causal capacity. Show that the analysis essay hills white causal capacity is greater than zero if and only if has a causal influence over essays, . We’ve just defined a notion of causal influence between two random variables in essay like white elephants, a causal model. What about when we say something like “Event A” causes “Event B”? What does this mean? Returning to the smoking-cancer example, it seems that we would say that smoking causes cancer provided , so that if someone makes the choice to smoke, uninfluenced by other causal factors, then they would increase their chance of cancer. Schoenberg And The By Carl Dahlhaus. Intuitively, it seems to me that this notion of events causing one another should be related to the notion of causal influence just defined above. But I don’t yet see quite how to do that. The first problem below suggests a conjecture in this direction: Suppose and are random variables in a causal model such that for some pair of values and analysis essay white elephants . Does this imply that exerts a causal influence on ? (Sum-over-paths for passions i have lived causal conditional probabilities?) I believe a kind of sum-over-paths formulation of analysis essay hills like white causal conditional probabilities is a modest essays possible, but haven’t worked out details.
The idea is as follows (the details may be quite wrong, but I believe something along these lines should work). Supose and analysis hills elephants are single vertices (with corresponding random variables) in a causal model. Then I would like to show first that if is not an ancestor of then , i.e., intervention does nothing. Second, if is an ancestor of then may be obtained by summing over all directed paths from to in , and a modest computing for each path a contribution to the sum which is a product of conditional probabilities along the path. (Note that we may need to analysis hills like white elephants consider the analysis lab report same path multiple times in the sum, since the random variables along the path may take different values). Analysis Hills. We used causal models in our definition of lab report causal conditional probabilities. But our informal definiton – imagine a hypothetical world in which it’s possible to force a variable to take a particular value – didn’t obviously require the use of a causal model. Indeed, in a real-world randomized controlled experiment it may be that there is no underlying causal model. This leads me to wonder if there is some other way of formalizing the informal definition we’ve given? Another way of framing the analysis hills like white last problem is that I’m concerned about the empirical basis for causal models. How should we go about constructing such models?
Are they fundamental, representing true facts about the resume approved world, or are they modelling conveniences? (This is by analysis hills like white no means a dichotomy.) It would be useful to when a formal work through many more examples, considering carefully the origin of the functions and of the auxiliary random variables . In this section we’ll develop a criterion that Pearl calls directional separation ( d-separation , for short). What d-separation does is let us inspect the graph of a causal model and conclude that a random variable in the model can’t tell us anything about the value of essay hills white another random variable in the model, or vice versa. To understand d-separation we’ll start with a simple case, and then work through increasingly complex cases, building up our intuition. I’ll conclude by giving a precise definition of d-separation, and by explaining how d-separation relates to the concept of conditional independence of random variables. Here’s the first simple causal model: Clearly, knowing can in resume approved, general tell us something about in this kind of analysis like white causal model, and three passions i have lived so in analysis essay hills like elephants, this case and are not d-separated. We’ll use the term d-connected as a synonym for “not d-separated”, and so in this causal model and are d-connected. By contrast, in the following causal model and don’t give us any information about and the essays dahlhaus, each other, and so they are d-separated: A useful piece of terminology is to say that a vertex like the middle vertex in this model is a collider for the path from to , meaning a vertex at which both edges along the path are incoming.
What about the causal model: In this case, it is possible that knowing will tell us something about , because of their common ancestry. It’s like the way knowing the genome for one sibling can give us information about the genome of another sibling, since similarities between the essay hills genomes can be inferred from the common ancestry. We’ll call a vertex like the three passions lived for essay middle vertex in this model a fork for essay hills white elephants the path from to , meaning a vertex at which both edges are outgoing. Construct an explicit causal model demonstrating the analysis lab report assertion of the last paragraph. For example, you may construct a causal model in which and analysis white are joined by new music by carl dahlhaus a fork, and where is actually a function of . Suppose we have a path from to essay like in a causal model. Let be the number of colliders along the path, and let be the resume approved number of forks along the analysis essay path.
Show that can only take the values or , i.e., the number of forks and colliders is a modest essays either the same or differs by at most one. We’ll say that a path (of any length) from to that contains a collider is a blocked path. By contrast, a path that contains no colliders is called an unblocked path. (Note that by the above exercise, an unblocked path must contain either one or no forks.) In general, we define and to be d-connected if there is an unblocked path between them. White Elephants. We define them to be d-separated if there is no such unblocked path. It’s worth noting that the concepts of d-separation and d-connectedness depend only on the graph topology and on which vertices and have been chosen.
In particular, they don’t depend on the nature of the random variables and , merely on the identity of the corresponding vertices. As a result, you can determine d-separation or d-connectdness simply by and the essays by carl dahlhaus inspecting the graph. This fact – that d-separation and d-connectdness are determined by the graph – also holds for analysis elephants the more sophisticated notions of d-separation and d-connectedness we develop below. With that said, it probably won’t surprise you to learn that the concept of d-separation is closely related to whether or not the random variables and are independent of one another. This is a connection you can (optionally) develop through the following exercises. I’ll state a much more general connection below. Suppose that and are d-separated. Show that and are independent random variables, i.e., that . Suppose we have two vertices which are d-connected in a graph . Explain how to construct a causal model on a modest proposal essays, that graph such that the analysis hills random variables and corresponding to schoenberg and the dahlhaus those two vertices are not independent. The last two exercises almost but don’t quite claim that random variables and in a causal model are independent if and only if they are d-separated.
Why does this statement fail to be true? How can you modify the statement to make it true? So far, this is pretty simple stuff. It gets more complicated, however, when we extend the notion of essay hills white elephants d-separation to cases where we are conditioning on lab report, already knowing the value of analysis essay like white elephants one or more random variables in the causal model. Resume Approved. Consider, for example, the graph: Now, if we know , then knowing doesn’t give us any additional information about , since by analysis like white elephants our original definition of resume approved a causal model is already a function of and some auxiliary random variables which are independent of . So it makes sense to say that blocks this path from to , even though in the unconditioned case this path would not have been considered blocked. We’ll also say that and analysis essay white elephants are d-separated, given . It is helpful to three i have give a name to vertices like the middle vertex in Figure A, i.e., to essay hills vertices with one ingoing and one outgoing edge.
We’ll call such vertices a traverse along the path from to a night all alone . Using this language, the lesson of the like white above discussion is that if is in a traverse along a path from to , then the three lived for essay path is blocked. By contrast, consider this model: In this case, knowing will in general give us additional information about , even if we know . This is analysis essay hills white because while blocks one path from to there is another unblocked path from to . A Night. And so we say that and essay hills like white are d-connected, given . Another case similar to Figure A is the model with a fork: Again, if we know , then knowing as well doesn’t give us any extra information about (or vice versa). So we’ll say that in resume approved, this case is blocking the analysis essay hills white elephants path from to all alone essay , even though in the unconditioned case this path would not have been considered blocked. Again, in this example and are d-separated, given . The lesson of this model is that if is located at a fork along a path from to essay like white , then the path is lived blocked. A subtlety arises when we consider a collider: In the unconditioned case this would have been considered a blocked path. And, naively, it seems as though this should still be the case: at analysis essay like white elephants first sight (at least according to my intuition) it doesn’t seem very likely that can give us any additional information about (or vice versa), even given that is known. Yet we should be cautious, because the a night all alone argument we made for the graph in Figure A breaks down: we can’t say, as we did for Figure A, that is a function of and analysis hills elephants some auxiliary independent random variables. In fact, we’re wise to be cautious because and really can tell us something extra about sieve, one another, given a knowledge of analysis essay hills like white . This is a phenomenon which Pearl calls Berkson’s paradox . He gives the example of a graduate school in music which will admit a student (a possibility encoded in resume approved, the value of analysis white elephants ) if either they have high undergraduate grades (encoded in sieve analysis lab report, ) or some other evidence that they are exceptionally gifted at music (encoded in ). It would not be surprising if these two attributes were anticorrelated amongst students in the program, e.g., students who were admitted on the basis of hills like white elephants exceptional gifts would be more likely than otherwise to have low grades.
And so in this case knowledge of (exceptional gifts) would give us knowledge of (likely to have low grades), conditioned on knowledge of (they were accepted into the program). Another way of seeing Berkson’s paradox is to construct an essay, explicit causal model for the graph in Figure B. Consider, for example, a causal model in which and are independent random bits, or , chosen with equal probabilities . We suppose that , where is addition modulo . This causal model does, indeed, have the structure of Figure B. But given that we know the value , knowing the value of white tells us everything about schoenberg and the essays by carl dahlhaus, , since . As a result of this discussion, in the causal graph of Figure B we’ll say that unblocks the path from to , even though in the unconditioned case the path would have been considered blocked. And we’ll also say that in this causal graph and are d-connected, conditional on essay hills like elephants, . The immediate lesson from the graph of Figure B is that and can tell us something about one another, given , if there is writing a formal essay a path between and where the only collider is at like white . In fact, the same phenomenon can occur even in this graph: To see this, suppose we choose and as in the example just described above, i.e., independent random bits, or , chosen with equal probabilities . We will let the unlabelled vertex be . And, finally, we choose . Resume Approved. Then we see as before that can tell us something about , given that we know , because . The general intuition about analysis white, graphs like that in Figure C is that knowing allows us to three passions i have lived for essay infer something about the ancestors of hills like elephants , and resume approved so we must act as though those ancestors are known, too. As a result, in essay hills like white, this case we say that unblocks the path from to lab report , since has an ancestor which is a collider on the path from to . And so in this case is d-connected to , given . Given the analysis essay like white elephants discussion of Figure C that we’ve just had, you might wonder why forks or traverses which are ancestors of can’t block a path, for three passions similar reasons? For instance, why don’t we consider and to be d-separated, given , in the following graph: The reason, of course, is that it’s easy to analysis essay hills construct examples where tells us something about in addition to what we already know from . And so we can’t consider and to be d-separated, given , in sieve lab report, this example.
These examples motivate the following definition: Definition: Let , and analysis essay like white elephants be disjoint subsets of vertices in a causal model. Consider a path from resume approved a vertex in to a vertex in . We say the analysis hills like elephants path is lab report blocked by if the path contains either: (a) a collider which is not an ancestor of , or (b) a fork which is in , or (c) a traverse which is in . We say the path is unblocked if it is hills white elephants not blocked. We say that and a formal are d-connected , given , if there is an unblocked path between some vertex in and some vertex in . and are d-separated , given , if they are not d-connected. Saying “ and are d-separated given ” is like elephants a bit of a mouthful, and so it’s helpful to have an abbreviated notation. We’ll use the abbreviation . Note that this notation includes the essay graph ; we’ll sometimes omit the graph when the context is clear. We’ll write to denote unconditional d-separation. As an aside, Pearl uses a similar but slightly different notation for d-separation, namely . Unfortunately, while the symbol looks like a LaTeX symbol, it’s not, but is most easily produced using a rather dodgy LaTeX hack.
Instead of using that hack over and over again, I’ve adopted a more standard LaTeX notation. While I’m making asides, let me make a second: when I was first learning this material, I found the hills like “d” for proposal essays “directional” in analysis essay elephants, d-separation and d-connected rather confusing. It suggested to me that the key thing was having a directed path from and the new music essays dahlhaus one vertex to the other, and that the complexities of colliders, forks, and so on were a sideshow. Of course, they’re not, they’re central to the whole discussion. For this reason, when I was writing these notes I considered changing the terminology to i-separated and i-connected, for analysis essay hills like elephants informationally-separated and informationally-connected. Resume Approved. Ultimately I decided not to do this, but I thought mentioning the issue might be helpful, in part to reassure readers (like me) who thought the “d” seemed a little mysterious. Okay, that’s enough asides, let’s get back to the main track of discussion. We saw earlier that (unconditional) d-separation is closely connected to the independence of random variables.
It probably won’t surprise you to learn that conditional d-separation is closely connected to conditional independence of random variables. Recall that two sets of random variables and are conditionally independent , given a third set of random variables , if . Analysis White Elephants. The following theorem shows that d-separation gives a criterion for when conditional independence occurs in a causal model: Theorem (graphical criterion for conditional independence): Let be a graph, and let , and be disjoint subsets of vertices in that graph. Then and are d-separated, given , if and analysis only if for all causal models on the random variables corresponding to essay hills like white and are conditionally independent, given . (Update: Thanks to Rob Spekkens for pointing out an error in my original statement of this theorem.) I won’t prove the theorem here.
However, it’s not especially difficult if you’ve followed the discussion above, and a night essay is a good problem to work through: The concept of d-separation plays a central role in the causal calculus. My sense is that it should be possible to find a cleaner and essay white more intuitive definition that substantially simplifies many proofs. It’d be good to spend some time trying to find such a definition. We’ve now got all the three i have concepts we need to hills state the rules of the causal calculus. There are three rules. The rules look complicated at first, although they’re easy to use once you get familiar with them.
For this reason I’ll start by explaining the proposal essays intuition behind the first rule, and essay like white how you should think about that rule. Having understood how to think about the first rule it’s easy to get the hang of all three rules, and so after that I’ll just outright state all three rules. In what follows, we have a causal model on a graph , and are disjoint subsets of the variables in the causal model. Recall also that denotes the and the new music perturbed graph in which all edges pointing to from the parents of have been deleted. This is the graph which results when an analysis essay white, experimenter intervenes to set the all alone value of , overriding other causal influences on hills like elephants, . Rule 1: When can we ignore observations: I’ll begin by i have lived for essay stating the first rule in all its glory, but don’t worry if you don’t immediately grok the whole rule. Instead, just take a look, and try to start getting your head around it. What we’ll do then is look at some simple special cases, which are easily understood, and gradually build up to an understanding of what the full rule is saying. Okay, so here’s the analysis essay white first rule of the writing essay causal calculus. What it tells us is that when , then we can ignore the observation of in computing the probability of , conditional on both and an intervention to set : To understand why this rule is true, and analysis like white what it means, let’s start with a much simpler case. Lived For Essay. Let’s look at what happens to the rule when there are no or variables in the mix.
In this case, our starting assumption simply becomes that is d-separated from in the original (unperturbed) graph . There’s no need to worry about because there’s no variable whose value is being set by intervention. In this circumstance we have , so is independent of . But the statement of the rule in this case is merely that , which is, indeed, equivalent to the standard definition of and analysis essay white elephants being independent. In other words, the first rule is simply a generalization of for essay what it means for and to be independent. The full rule generalizes the notion of independence in white, two ways: (1) by adding in lab report, an extra variable whose value has been determined by passive observation; and (2) by adding in an extra variable whose value has been set by intervention. Analysis Essay Like White Elephants. We’ll consider these two ways of generalizing separately in the next two paragraphs. We begin with generalization (1), i.e., there is no variable in new music, the mix. In this case, our starting assumption becomes that is d-separated from , given , in the graph . Analysis Essay Elephants. By the graphical criterion for conditional independence discussed in the last section this means that is conditionally independent of , given , and so , which is exactly the three passions i have lived statement of the rule.
And so the first rule can be viewed as a generalization of what it means for and to analysis like elephants be independent, conditional on a modest essays, . Now let’s look at the other generalization, (2), in which we’ve added an extra variable whose value has been set by intervention, and where there is no variable in the mix. Analysis White. In this case, our starting assumption becomes that is d-separated from , given , in the perturbed graph . Three Passions For Essay. In this case, the graphical criterion for conditional indepenence tells us that is hills like white elephants independent from , conditional on and the new music essays, the value of analysis essay hills like white elephants being set by experimental intervention, and so . Again, this is exactly the when writing a formal statement of the analysis hills like white rule. The full rule, of course, merely combines both these generalizations in i have lived for essay, the obvious way. It is really just an essay like, explicit statement of the content of the graphical criterion for conditional independence, in a context where has been observed, and the value of set by experimental intervention. The rules of the causal calculus: All three rules of the resume approved causal calculus follow a similar template to the first rule: they provide ways of using facts about the causal structure (notably, d-separation) to make inferences about conditional causal probabilities. I’ll now state all three rules.
The intuition behind rules 2 and 3 won’t necessarily be entirely obvious, but after our discussion of rule 1 the remaining rules should at least appear plausible and comprehensible. I’ll have bit more to say about intuition below. As above, we have a causal model on a graph , and are disjoint subsets of the hills like elephants variables in the causal model. denotes the perturbed graph in which all edges pointing to from the a formal parents of essay hills like white have been deleted. denotes the graph in which all edges pointing out from to the children of have been deleted. We will also freely use notations like to denote combinations of these operations. Rule 1: When can we ignore observations: Suppose . Then: Rule 2: When can we ignore the act of intervention: Suppose . Then: Rule 3: When can we ignore an intervention variable entirely: Let denote the set of nodes in which are not ancestors of . Suppose . Three Passions I Have For Essay. Then: In a sense, all three rules are statements of conditional independence.
The first rule tells us when we can ignore an observation. Hills. The second rule tells us when we can ignore the act of intervention (although that doesn’t necessarily mean we can ignore the value of the variable being intervened with). And the third rule tells us when we can ignore an passions for essay, intervention entirely, both the act of intervention, and the value of the variable being intervened with. I won’t prove rule 2 or rule 3 – this post is analysis hills like white elephants already quite long enough. (If I ever significantly revise the writing a formal essay post I may include the proofs). The important thing to elephants take away from these rules is that they give us conditions on writing essay, the structure of causal models so that we know when we can ignore observations, acts of intervention, or even entire variables that have been intervened with. Analysis White Elephants. This is resume approved obviously a powerful set of hills white tools to three lived for essay be working with in manipulating conditional causal probabilities! Indeed, according to Pearl there’s even a sense in hills like white elephants, which this set of rules is complete , meaning that using these rules you can identify all causal effects in and the new music dahlhaus, a causal model. I haven’t yet understood the proof of this result, or even exactly what it means, but thought I’d mention it. The proof is in hills like white elephants, papers by Shpitser and Pearl and Huang and Valtorta. If you’d like to see the proofs of the rules of the writing a formal calculus, you can either have a go at proving them yourself, or you can read the proof. Suppose the conditions of essay white elephants rules 1 and analysis 2 hold.
Can we deduce that the conditions of rule 3 also hold? Using the analysis essay causal calculus to analyse the smoking-lung cancer connection. We’ll now use the causal calculus to analyse the connection between smoking and lung cancer. Earlier, I introduced a simple causal model of i have lived this connection: The great benefit of this model was that it included as special cases both the analysis essay hypothesis that smoking causes cancer and the hypothesis that some hidden causal factor was responsible for both smoking and cancer. It turns out, unfortunately, that the causal calculus doesn’t help us analyse this model. I’ll explain why that’s the case below. However, rather than worrying about this, at essays dahlhaus this stage it’s more instructive to analysis hills elephants work through an example showing how the causal calculus can be helpful in analysing a similar but slightly modified causal model. New Music By Carl. So although this modification looks a little mysterious at first, for hills like white elephants now I hope you’ll be willing to accept it as given. The way I’m going to modify the resume approved causal model is by introducing an extra variable, namely, whether someone has appreciable amounts of tar in analysis like white elephants, their lungs or not: (By tar, I don’t mean “tar” literally, but rather all the material deposits found as a result of smoking.)
This causal model is a plausible modification of the original causal model. Passions I Have Lived. It is at least plausible to like white suppose that smoking causes tar in the lungs and that those deposits in turn cause cancer. But if the hidden causal factor is genetic, as the tobacco companies argued was the case, then it seems highly unlikely that the genetic factor caused tar in the lungs, except by the indirect route of causing those people to smoke. (I’ll come back to what happens if you refuse to all alone essay accept this line of reasoning. For now, just go with it.) Our goal in this modified causal model is to compute probabilities like . What we’ll show is that the causal calculus lets us compute this probability entirely in hills like, terms of probabilities like and other probabilities that don’t involve an intervention, i.e., that don’t involve . This means that we can determine without needing to passions lived know anything about the hidden factor. We won’t even need to know the analysis white nature of the hidden factor. It also means that we can determine without needing to intervene to force someone to smoke or not smoke, i.e., to schoenberg and the new music by carl dahlhaus set the value for . In other words, the causal calculus lets us do something that seems almost miraculous: we can figure out the probability that someone would get cancer given that they are in the smoking group in a randomized controlled experiment, without needing to analysis hills like elephants do the when writing essay randomized controlled experiment. And this is true even though there may be a hidden causal factor underlying both smoking and cancer. Okay, so how do we compute ? The obvious first question to ask is whether we can apply rule 2 or rule 3 directly to the conditional causal probability . If rule 2 applies, for example, it would say that intervention doesn’t matter, and so . Intuitively, this seems unlikely. We’d expect that intervention really can change the probability of essay white cancer given smoking, because intervention would override the three hidden causal factor.
If rule 3 applies, it would say that , i.e., that an intervention to force someone to smoke has no impact on whether they get cancer. This seems even more unlikely than rule 2 applying. However, as practice and a warm up, let’s work through the details of seeing whether rule 2 or rule 3 can be applied directly to analysis essay hills like elephants . For rule 2 to apply we need . To check whether this is true, recall that is the graph with the edges pointing out from deleted: Obviously, is not d-separated from in this graph, since and a modest essays have a common ancestor. This reflects the fact that the hidden causal factor indeed does influence both and . So we can’t apply rule 2.
What about rule 3? For this to essay white elephants apply we’d need . Recall that is the graph with the edges pointing toward deleted: Again, is not d-separated from , in this case because we have an unblocked path directly from to . This reflects our intuition that the value of can influence , even when the value of has been set by intervention. So we can’t apply rule 3. Okay, so we can’t apply the rules of the causal calculus directly to determine . Is there some indirect way we can determine this probability? An experienced probabilist would at this point instinctively wonder whether it would help to condition on the value of , writing: Of course, saying an experienced probabilist would instinctively do this isn’t quite the same as explaining why one should do this! However, it is at i have for essay least a moderately obvious thing to do: the essay hills like white only extra information we potentially have in by carl, the problem is , and so it’s certainly somewhat natural to try to introduce that variable into the problem. As we shall see, this turns out to be a wise thing to do.
I used without proof the equation . This should be intuitively plausible, but really requires proof. Prove that the equation is hills white correct. To simplify the right-hand side of equation , we first note that we can apply rule 2 to the second term on the right-hand side, obtaining . To check this explicitly, note that the condition for rule 2 to proposal essays apply is that . We already saw the graph above, and, indeed, is d-separated from in that graph, since the only path from to is blocked at . Hills Elephants. As a result, we have: At this point in the presentation, I’m going to speed the discussion up, telling you what rule of the calculus to apply at each step, but not going through the process of explicitly checking that the conditions of the rule hold. (If you’re doing a close read, you may wish to check the conditions, however.) The next thing we do is to apply rule 2 to a night all alone the first term on the right-hand side of equation , obtaining . We then apply rule 3 to remove the , obtaining . Substituting back in analysis essay white elephants, gives us:
So this means that we’ve reduced the computation of to the computation of . This doesn’t seem terribly encouraging: we’ve merely substituted the computation of one causal conditional probability for another. Still, let us continue plugging away, and see if we can make progress. The obvious first thing to try is to dahlhaus apply rule 2 or rule 3 to simplify . Unfortunately, though not terribly surprisingly, neither rule applies. Analysis Essay White Elephants. So what do we do? Well, in a repeat of resume approved our strategy above, we again condition on essay white elephants, the other variable we have available to us, in sieve analysis lab report, this case : Now we’re cooking!
Rule 2 lets us simplify the first term to , while rule 3 lets us simplify the second term to , and so we have . To substitute this expression back into equation  it helps to change the summation index from to , since otherwise we would have a duplicate summation index. This gives us: This is the analysis essay white elephants promised expression for (i.e., for probabilities like , assuming the schoenberg and the new music by carl dahlhaus causal model above) in terms of quantities which may be observed directly from experimental data, and which don’t require intervention to do a randomized, controlled experiment. Once is determined, we can compare it against analysis white . Essay. If is analysis essay white larger than then we can conclude that smoking does, indeed, play a causal role in cancer. Something that bugs me about the derivation of equation  is that I don’t really know how to “see through” the calculations. Yes, it all works out in a modest, the end, and it’s easy enough to follow along. Yet that’s not the same as having a deep understanding. Too many basic questions remain unanswered: Why did we have to condition as we did in the calculation?
Was there some other way we could have proceeded? What would have happeed if we’d conditioned on the value of the hidden variable? (This is essay like white not obviously the resume approved wrong thing to do: maybe the hidden variable would ultimately drop out of the calculation). Why is it possible to analysis essay white compute causal probabilities in this model, but not (as we shall see) in the model without tar? Ideally, a deeper understanding would make the answers to when a formal essay some or all of these questions much more obvious. Why is it so much easier to essay hills like elephants compute than in the model above? Is there some way we could have seen that this would be the case, without needing to go through a detailed computation? Suppose we have a causal model , with a subset of vertices for which all conditional probabilities are known.
Is it possible to give a simple characterization of for resume approved which subsets and of vertices it is essay hills like possible to compute using just the conditional probabilities from ? Unfortunately, I don’t know what the experimentally observed probabilities are in the smoking-tar-cancer case. If anyone does, I’d be interested to know. In lieu of actual data, I’ll use some toy model data suggested by Pearl; the data is sieve quite unrealistic, but nonetheless interesting as an illustration of the analysis essay hills white use of equation . The toy model data is as follows: (1) 47.5 percent of the population are nonsmokers with no tar in their lungs, and 10 percent of resume approved these get cancer. (2) 2.5 percent are smokers with no tar, and 90 percent get cancer. (3) 2.5 percent are nonsmokers with tar, and 5 percent get cancer. (4) 47.5 percent are smokers with tar, and white 85 percent get cancer. In this case, we get:
By contrast, percent, and so if this data was correct (obviously it’s not even close) it would show that smoking actually somewhat reduces a person’s chance of getting lung cancer. Resume Approved. This is despite the fact that percent, and like white so a naive approach to a modest causality based on correlations alone would suggest that smoking causes cancer. In fact, in this imagined world smoking might actually be useable as a preventative treatment for cancer! Obviously this isn’t truly the case, but it does illustrate the power of analysis like white elephants this method of analysis. Summing up the new music by carl general lesson of the smoking-cancer example, suppose we have two competing hypotheses for the causal origin of hills white elephants some effect in a system, A causes C or B causes C, say.
Then we should try to construct a realistic causal model which includes both hypotheses, and then use the causal calculus to a modest essays attempt to analysis like distinguish the relative influence of the two causal factors, on the basis of experimentally accessible data. Incidentally, the kind of analysis of smoking we did above obviously wasn’t done back in the 1960s. I don’t actually know how causality was established over the protestations that correlation doesn’t impy causation. A Modest Proposal Essays. But it’s not difficult to think of ways you might have come up with truly convincing evidence that smoking was a causal factor. One way would have been to analysis essay hills like white look at the incidence of schoenberg and the new music by carl dahlhaus lung cancer in populations where smoking had only recently been introduced. Suppose, for example, that cigarettes had just been introduced into the (fictional) country of Nicotinia, and that this had been quickly followed by a rapid increase in rates of lung cancer. If this pattern was seen across many new markets then it would be very difficult to argue that lung cancer was being caused solely by essay hills like some pre-existing factor in the population. Construct toy model data where smoking increases a person’s chance of getting lung cancer. Let’s leave this model of smoking and lung cancer, and come back to our original model of smoking and lung cancer: What would have happened if we’d tried to use the causal calculus to analyse this model? I won’t go through all the details, but you can easily check that whatever rule you try to apply you quickly run into a dead end.
And so the causal calculus doesn’t seem to three lived for essay be any help in analysing this problem. This example illustrates some of the limitations of the causal calculus. In order to compute we needed to assume a causal model with a particular structure: While this model is plausible, it is not beyond reproach. You could, for example, criticise it by analysis white saying that it is not the presence of tar deposits in the lungs that causes cancer, but maybe some other factor, perhaps something that is essay currently unknown. This might lead us to consider a causal model with a revised structure: So we could try instead to use the causal calculus to analysis analyse this new model. I haven’t gone through this exercise, but I strongly suspect that doing so we wouldn’t be able to use the rules of the i have causal calculus to compute the relevant probabilities. The intuition behind this suspicion is that we can imagine a world in which the analysis white elephants tar may be a spurious side-effect of essays smoking that is in fact entirely unrelated to essay like elephants lung cancer. What causes lung cancer is really an entirely different mechanism, but we couldn’t distinguish the two from the resume approved statistics alone.
The point of this isn’t to say that the causal calculus is useless. It’s remarkable that we can plausibly get information about the outcome of a randomized controlled experiment without actually doing anything like that experiment. But there are limitations. To get that information we needed to make some presumptions about the causal structure in essay hills like, the system. Those presumptions are plausible, but not logically inevitable. If someone questions the presumptions then it may be necessary to i have lived for essay revise the model, perhaps adopting a more sophisticated causal model. One can then use the hills white elephants causal calculus to attempt to analysis analyse that more sophisticated model, but we are not guaranteed success. Essay Hills White Elephants. It would be interesting to understand systematically when this will be possible and when it will not be. The following problems start to get at some of the a modest proposal essays issues involved. Is it possible to essay like white make a more precise statement than “the causal calculus doesn’t seem to be any help” for the original smoking-cancer model? Given a probability distribution over some random variables, it would be useful to have a classification theorem describing all the causal models in which those random variables could appear.
Extending the last problem, it’d be good to have an algorithm to answer questions like: in the space of sieve lab report all possible causal models consistent with a given set of observed probabilities, what can we say about the white possible causal probabilities? It would also be useful to be able to input to the algorithm some constraints on the causal models, representing knowledge we’re already sure of. In real-world experiments there are many practical issues that must be addressed to passions i have lived design a realiable randomized, controlled experiment. These issues include selection bias, blinding, and many others. There is an entire field of experimental design devoted to addressing such issues. By comparison, my description of causal inference ignores many of these practical issues. Can we integrate the best thinking on analysis hills like white, experimental design with ideas such as causal conditional probabilities and i have lived for essay the causal calculus? From a pedagogical point of view, I wonder if it might have been better to work fully through the smoking-cancer example before getting to the abstract statement of the rules of the causal calculus. Those rules can all be explained and motivated quite nicely in essay hills white elephants, the context of the smoking-cancer example, and all alone essay that may help in understanding. I’ve described just a tiny fraction of the work on essay white, causality that is now going on.
My impression as an sieve analysis, admittedly non-expert outsider to the field is that this is an exceptionally fertile field which is developing rapidly and giving rise to many fascinating applications. Over the next few decades I expect the theory of causality will mature, and be integrated into like the foundations of disciplines ranging from economics to medicine to essays social policy. Causal discovery: One question I’d like to understand better is how to discover causal structures inside existing data sets. After all, human beings do a pretty good (though far from perfect) job at figuring out causal models from their observation of the world. Essay Like White Elephants. I’d like to better understand how to use computers to automatically discover such causal models. I understand that there is already quite a literature on proposal essays, the automated discovery of causal models, but I haven’t yet looked in much depth at that literature. I may come back to it in a future post. I’m particularly fascinated by the idea of analysis essay hills like white extracting causal models from very large unstructured data sets. Schoenberg And The New Music. The KnowItAll group at the University of Washington (see Oren Etzioni on analysis essay hills like elephants, Google Plus) have done fascinating work on a related but (probably) easier problem, the problem of resume approved open information extraction. This means taking an analysis essay like white, unstructured information source (like the web), and analysis using it to analysis hills like white elephants extract facts about the real world. A Night Essay. For instance, using the web one would like computers to be able to learn facts like “Barack Obama is analysis essay like President of the United States”, without needing a human to feed it that information.
One of the things that makes this task challenging is all the three i have lived for essay misleading and difficult-to-understand information out on the web. For instance, there are also webpages saying “George Bush is analysis President of the a formal United States”, which was probably true at the time the pages were written, but which is now misleading. We can find webpages which state things like “[Let’s imagine] Steve Jobs is essay elephants President of the United States“; it’s a difficult task for analysis an unsupervised algorithm to figure out how to interpret that “Let’s imagine”. Analysis Like White. What the KnowItAll team have done is made progress on figuring out how to all alone essay learn facts in such a rich but uncontrolled environment. What I’m wondering is whether such techniques can be adapted to extract causal models from data?
It’d be fascinating if so, because of course humans don’t just reason with facts, they also reason with (informal) causal models that relate those facts. Perhaps causal models or a similar concept may be a good way of white elephants representing some crucial part of our knowledge of the world. What systematic causal fallacies do human beings suffer from? We certainly often make mistakes in the causal models we extract from our observations of the world – one example is that we often do assume that correlation implies causation, even when that’s not true – and it’d be nice to understand what systematic biases we have. Humans aren’t just good with facts and causal models. We’re also really good at juggling multiple causal models, testing them against schoenberg new music essays dahlhaus one another, finding problems and inconsistencies, and making adjustments and integrating the results of those models, even when the results conflict. In essence, we have a (working, imperfect) theory of how to essay hills like white deal with causal models.
Can we teach machines to do this kind of integration of causal models? We know that in and the new music dahlhaus, our world the sun rising causes the rooster to crow, but it’s possible to essay white imagine a world in which it is the rooster crowing that causes the sun to rise. This could be achieved in a suitably designed virtual world, for example. The reason we believe the first model is correct in our world is not intrinsic to sieve analysis lab report the data we have on roosters and sunrise, but rather depends on a much more complex network of background knowledge. For instance, given what we know about roosters and the sun we can easily come up with plausible causal mechanisms (solar photons impinging on the rooster’s eye, say) by which the sun could cause the rooster to crow. Analysis Like Elephants. There do not seem to be any similarly plausible causal models in the other direction.
How do we determine what makes a particular causal model plausible or not? How do we determine the class of resume approved plausible causal models for analysis hills like a given phenomenon? Can we make this kind of judgement automatically? (This is all closely related to the last problem). Continuous-time causality: A peculiarity in schoenberg essays by carl dahlhaus, my post is that even though we’re talking about causality, and time is analysis essay presumably important, I’ve avoided any explicit mention of time. Of course, it’s implicitly there: if I’d been a little more precise in specifying my models they’d no doubt be conditioned on analysis lab report, events like “smoked at least a pack a day for 10 or more years”.
Of course, this way of analysis essay like white elephants putting time into new music dahlhaus the picture is analysis essay hills white elephants rather coarse-grained. In a lot of practical situations we’re interested in understanding causality in a much more temporally fine-grained way. Schoenberg And The By Carl. To explain what I mean, consider a simple model of the relationship between what we eat and our insulin levels: This model represents the fact that what we eat determines our insulin levels, and analysis essay our insulin levels in a modest proposal, turn play a part in determining how hungry we feel, and thus what we eat. But as a model, it’s quite inadequate.
In fact, there’s a much more complex feedback relationship going on, a constant back-and-forth between what we eat at any given time, and analysis essay hills like white elephants our insulin levels. Three I Have For Essay. Ideally, this wouldn’t be represented by essay elephants a few discrete events, but rather by a causal model that reflects the continual feedback between these possibilities. What I’d like to proposal essays see developed is a theory of continuous-time causal models, which can address this sort of issue. Analysis Essay White Elephants. It would also be useful to extend the calculus to continuous spaces of events. So far as I know, at present the causal calculus doesn’t work with these kinds of ideas. Can we formulate theories like electromagnetism, general relativity and quantum mechanics within the framework of the causal calculus (or some generalization)? Do we learn anything by doing so? Other notions of causality: A point I’ve glossed over in the post is how the notion of a modest causal influence we’ve been studying relates to other notions of causality. The notion we’ve been exploring is based on the notion of causality that is established by a (hopefully well-designed!) randomized controlled experiment.
To understand what that means, think of what it would mean if we used such an experiment to establish that smoking does, indeed, cause cancer. All this means is that in analysis essay like white elephants, the population being studied , forcing someone to smoke will increase their chance of getting cancer. Now, for the practical matter of three setting public health policy, that’s obviously a pretty important notion of causality. But nothing says that we won’t tomorrow discover some population of people where no such causal influence is found. Or perhaps we’ll find a population where smoking actively helps prevent cancer. Both these are entirely possible.
What’s going on is that while our notion of causality is useful for some purposes, it doesn’t necessarily say anything about the details of an underlying causal mechanism, and analysis elephants it doesn’t tell us how the results will apply to sieve other populations. In other words, while it’s a useful and important notion of analysis like causality, it’s not the only way of thinking about causality. Something I’d like to do is to sieve lab report understand better what other notions of causality are useful, and analysis essay hills elephants how the intervention-based approach we’ve been exploring relates to sieve analysis lab report those other approaches. Thanks to Jen Dodd, Rob Dodd, and analysis white elephants Rob Spekkens for many discussions about causality. Especial thanks to schoenberg new music essays Rob Spekkens for pointing me toward the epilogue of Pearl’s book, which is what got me hooked on causality! Principal sources and further reading. A readable and stimulating overview of essay hills like causal inference is the epilogue to Judea Pearl’s book. The epilogue, in turn, is based on a survey lecture by Pearl on causal inference.
I highly recommend getting a hold of the when writing a formal essay book and reading the epilogue; if you cannot do that, I suggest looking over like white, the survey lecture. A draft copy of the resume approved first edition of the entire book is available on Pearl’s website. Unfortunately, the draft does not include the analysis like full text of the epilogue, only the survey lecture. The lecture is still good, though, so you should look at it if you don’t have access to the full text of the essay epilogue. I’ve also been told good things about the book on causality by Spirtes, Glymour and Scheines, but haven’t yet had a chance to have a close look at it. An unfortunate aspect of the current post is that it gives the impression that the theory of causal inference is entirely Judea Pearl’s creation. Of course that’s far from the case, a fact which is quite evident from both Pearl’s book, and the Spirtes-Glymour-Scheines book.
However, the particular facets I’ve chosen to focus on essay hills white, are due principally to schoenberg essays by carl Pearl and his collaborators: most of the current post is based on chapter 3 and chapter 1 of Pearl’s book, as well as a 1994 paper by Pearl, which established many of the key ideas of the causal calculus. Finally, for an enjoyable and informative discussion of analysis like some of the challenges involved in understanding causal inference I recommend Jonah Lehrer’s recent article in Wired . Interested in more? Please subscribe to this blog, or follow me on Twitter. You may also enjoy reading my new book about open science, Reinventing Discovery. Do you think there’d be a way to interpret causal structure via geometry, much like we use geometry to express correlation and other patterns in data mining. Sieve. The geometry might have to be something that encodes causality – maybe a manifold with negative signature ? @Suresh – Fascinating idea! No idea if it’s possible, though, the thought never crossed my mind. Essay Hills Elephants. I guess I think of causal models as having an inherent directionality, due to the dag structure, while most geometries don’t have the same kind of directionality. But maybe there’s some trick to get around that. There’s been plenty of work on three passions i have lived for essay, the geometry of curved exponential families, and their relation to inference in graphical models. Analysis Hills White. See, as a start, e.g.
Bernd Sturmfels and Lior Pachter also have a pretty good book that touches on a lot of this — Yes, I’m aware of three passions i have that work. But the geometry there is like white a geometry in three passions i have lived, the parameter space. I don’t think it can be used to capture this kind of causality (at least at essay elephants first glance) I came across this as I was interested in oral thrush. The NHS guidance (quite reasonably) states that a high proportion of AIDS patients have thrush. Thrush has many causes and is correlated with use of resume approved inhaled steroids. I read the article without a second thought – it seemed correct and balanced. But commenters assumed that thrush had a high probably of being caused by aids and that it was highly irresponsible not to say it could also be caused by steroids. This is a typical example of analysis essay white elephants Bayes – the a priori chance of having AIDS is lower (I think) than being on Oral steroids.
I don’t know the a modest proposal essays answer. I don’t think the human race can eveolve genetically to process probabilities correctly, so it has to be education at an early age! That’s another nice example, and of a type that I suspect often infects policy-making and public discussion. 1. Analysis Essay Hills White. If there’s an essay, alternative . Like White Elephants. path from smoking to lung cancer it may be possible to put bounds on P(cancer|dio(smoking)) even if you can’t compute it exactly. 2. Similar graphs can be constructed for quantum amplitudes instead of (and in a night essay, addition to) probabilities. It might be interesting to analyse EPR and other experiments in this way, especially from the analysis essay like elephants point of view of schoenberg and the by carl dahlhaus hidden variable models of QM.
Thanks for this very informative post. Let me just make a few comments about your “physics” question: “Can we formulate theories like electromagnetism, general relativity and quantum mechanics within the framework of the causal calculus (or some generalization)? Do we learn anything by doing so?” I have been working on formulating quantum theory in a Bayesian network language, which is an obvious precursor to analysis white developing a causal calculus for it. Even that problem is not so simple, given that the standard formalism has an resume approved, assumed causal structure built into it, which we need to get rid of before we start. My recent papers with Rob Spekkens are part of an like white elephants, attempt to do that.
One lesson that I have learned from proposal this is that we need to get away from the usual “initial state+dynamics” way of looking at physics in order to fit it into this framework. Any correlations that exist in the initial state have to be modelled explicitly in the causal network because it assumes that the root vertices are independent. Finally, let me just mention that you might be able to hills like elephants get away with a simpler structure for modelling causality in deterministic theories like electromagnetism. Directed acyclic graphs are needed in general in order to all alone model non-Markovian causal processes, but deterministic theories (and unitary evolution in quantum theory) are necessarily Markovian. Therefore, you should be able to essay elephants get away with just using a poset to model causality in when a formal, these cases, the analysis hills like corresponding DAG being just the Hasse diagram of the poset. It is much easier to sieve analysis deal with continuous posets than continuous generalizations of graphs, so this could be a good first step.
By the way, this explains why Raphael Sorkin et. al. Essay. are able to get away with just using posets in the causal set approach to quantum gravity, because they only care about global unitary evolution. Thanks for the pointer to your work, Matt, it sounds fascinating. Although I’ve chatted with Rob about this, I didn’t realize that you were trying to formulate quantum theory in sieve analysis lab report, terms of Bayesian networks. (He may well have mentioned it, but I perhaps didn’t understand what he was saying – I hadn’t read Pearl at all at that time – and so forgot.) Nice exposition! Perhaps some notion of “latent surprise” could be relevant.
Adapting from the Wired article you cite, imagine that a candidate drug’s operation has two plausible causal models. Hills Elephants. The first and most plausible model is simple. It is used during drug development. Resume Approved. The second-most plausible model is complex (but still plausible if one analyzes it). If that second-most plausible causal model is hills like elephants very different from the first, that could be a “latent surprise” for and the new music by carl dahlhaus researchers – a warning that, if their understanding of the drug’s operation changes somewhat, the clinical effects could be profound. In general, if the most plausible few models are close (in the metric of plausibility) yet very different (in the metric space of causal model similarity), this is a warning of analysis essay hills elephants big latent surprises if our understanding shifts a bit. Suppose that, as you speculate, we could automatically “determine the class of schoenberg and the essays by carl plausible causal models for a given phenomenon”. We might then also be able to scan automatically for latent surprises in analysis white, important systems: scientific, social, financial, policy, and so forth. You mentioned the following: “Obviously, it’d make no sense to have loops in sieve lab report, the graph: We can’t have causing causing causing ! At least, not without a time machine.” Loops in causality DAG can be created without time machines as follows. 1. In some distant origin that is not in the history of measurements, A caused B;
4. so on and so forth. 5. Over time, A, B, and essay hills like C have caused other variables due to unknown reasons. So, to the observer, A caused B, which caused C, which (in turn) caused A. Resume Approved. This situation could happen in Human History due to lapses in measurement and in Astronomy because the lifetime of the observed (universe) is much longer than the lifetime of the essay white elephants observer (humans). Thanks for this interesting post, which provides a nice concise introduction to causal calculus. There is one interesting aspect to this whole chain of reasoning based on resume approved, randomized controlled trials as the basis of empirical causality that I haven’t seen discussed yet: a controlled trial assumes that the experimenter is an agent possessing free will, and is thus outside of any causal model. There is a recent tendency in essay hills elephants, the scientific community (see this article for example, and my comments on it) to claim that free will does not exist, and that human behavior is governed entirely by molecular processes (and thus ultimately quantum physics). With that assumption, whatever an resume approved, experimenter does is merely one more observable in a stochastic network, randomized controlled trials disappear, and causal calculus disappears as well. We arrive at the conclusion that the only scientific method to attribute causality relies on the existence of free will as a source of “obvious” causality. But then, as you show, there are causal models from which the experimenter’s intervention can be eliminated. We can thus draw conclusions about causality without assuming the “obvious” source of free will.
I wonder if it is like white elephants possible to when writing essay state under which conditions a causal model permits this elimination. Rules 2 and 3 are about individual variables, but is analysis essay hills white elephants there a rule that applies to a complete graph? Thanks for this. I’ve been spending a lot of time thinking about Pearl’s book lately and this is by far the most accessible introduction to the material that I have come across. One quick correction. Proposal. Close to the end of your discussion of rule 1 (2 paragraphs before the heading: “the rules of the causal calculus”), you give the equation:
Presumably you mean: Thanks, I’ve corrected it! “Business Week recently ran an spoof article pointing out some amusing examples of the dangers of inferring correlation from causation.” Probably you meant the other way around: “amusing examples of the analysis essay white dangers of inferring causation from correlation”? I have enjoyed a lot reading this. I am slightly confused about the wording of the following sentence: where f_j is a function, and a night essay Y_j is a collection of random variables such that: (a) the Y_j,. are independent of one another for different values of j; and (b) for each j, Y_j,. is independent of all variables X_k, except when X_k is analysis essay hills like X_j itself, or a descendant of X_j. The intuition is that the are a collection of auxiliary random variables which inject some extra randomness into X_j (and, through X_j, its descendants), but which are otherwise independent of the variables in the causal model.
What you mean by that is that for instance in the diagram above the paragraph Y_4,i is not independent of X_3 and X_2? No the Y_4,i’s are independent of X_3 and X_2. The only way this could fail is if condition (b) is met. That condition tells us that Y_4,i may not be independent of X_k when X_k is X_4 or a descendant. In that particular diagram, X_4 has no descendants, so we merely have Y_4,i not a descendant of X_4. Thanks for sieve analysis writing this up. It was very helpful! Regarding eq , you commented that it wasn’t transparent. Analysis Essay Hills Like Elephants. If I’m not mistake, you can reduce this to.
which is a modest proposal much more transparent. How do you do this? My mistake. I thought I had marginalized out the elephants x’, but didn’t. one famous place case study where “hidden causality” is notoriously, even fiendishly difficult to isolate and shows the extreme subtlety involved: local hidden variable theories for quantum mechanics. which recently have been brought back from the dead (or maybe semi zombie state) by anderson/brady in resume approved, a soliton model. Essay. more thoughts on resume approved, that here. Essay Hills. it has an aura of unorthodoxy but lets not forget that the a night greats have always been enamored with the hills like white elephants idea. einstein, schroedinger, ‘t hooft, etcetera. part of the resume approved difficulty in analysis hills like, QM is the idea of counterintuitive variables that might actually cause the experiment apparatus to “measure” or “not measure” (or “click” vs “not click/silent”). this has been called a “conspiracy” for decades. not sure who invented that description.
Goes into causal detection based upon resume approved, ‘prediction when variable A has been removed’, and why correlation sometimes makes causal detection worse, not better. Imply causation? I think this has been an issue for some time now because, frankly, causality cannot be proven. Essay Hills White. What science engages in is probablistic hypothetical inductive empiricism – in short, we can never know causality no matter how much some scientists would like you to believe. Science today is merely a refined scholasticism, that just so happened to plague humanity for nearly 2000 years. Essays. Not a single person can or has or will prove (analytically) universal causality of analysis essay like Being – to put it in easier terms, someone prove to me gravity will exist next Tuesday… Interesting article overall, but I disagree with this statement: We can’t have X causing Y causing Z causing Y! In fact, this is i have lived called positive feedback loop and is common in nature. Analysis Like Elephants. You will find a lot of examples in wikipedia, none of them needs a time machine #128521; I noticed I incorrectly quoted you above, but the point is, loops in causal diagrams are common.
The labels in the diagrams aren’t just for broad classes of a night all alone phenomena, they’re labels for random variables. A reasonable informal way of thinking is that this means you should think of the nodes as referring to specific events. Suppose you have a feedback loop: Eating chocolate = causes Mark to analysis essay like white gain weight = reduced tolerance for glucose = Eating chocolate (etc). The second “Eating chocolate” is actually a later event, which would be associated with a separate random variable, and would have a separate node in a causal diagram. Incidentally, that informal way of sieve lab report thinking – nodes as specific events in analysis essay white elephants, time – isn’t the full story.
You really need to schoenberg and the essays dahlhaus understand the analysis essay white technical definition of a random variable. But this informal approach conveys the gist of what’s going on. In , I’m confused how to expand the right side; I don’t see where I can get the values for pa(Xj). I’m trying to expand the basic cancer-smoking-hidden model in terms of basic probabilities, and I can only get as far as P(gets cancer | do(smokes)) = P(gets cancer, smokes) / P(smokes | pa(Smoke)). (My end goal is to a night see if I can use  to expand the cancer-smoking-tar-hidden model and obtain the essay like same result that you did, but without using the causal calculus.) pa(.) is just used to denote the parents of a node (or collection of nodes) in the causal graph. I had previously heard one of Pearl’s talks and I took a course in graphical models, but I really understood the Pearl’s ideas better after reading your post. Thanks. Hello, thanks for this nice explanation of resume approved Pearl’s al. theory. But there is analysis hills white something I can’t grasp in spite of reading Pearl’s lecture slides or some parts of all alone his papers. When simplifying equation , you say (as Pearl does) that we can apply rule 2 to find : p(z|do(x)) = p(z|x) But rule 2 is much more complex than this.
It tells about x,y,z and w. How can you make disappear y and analysis white elephants w in rule 2 ? Is it because w is unobserved ? Is it because pa(y) = x and resume approved we can use another relation ? Thanks for your help. Okay, after many readings , I guess I’m now able to answer to myself. In the 1992 paper, Pearl derives three properties from  formula. p(z|do(x)) = p(z|x) iff z_|_ pa(x) | x. which is the case in the example graph.
Though Pearl says that rule 2 is equivalent to this property, I think the latter is much more powerful ! I am trying to understand your eq. ; when I set up the calculations in a spreadsheet table, I get the following result, namely no difference between P(cancer) and P(cancer|do(smoking)), which is what I intuitively expected. Can you tell me where I went wrong? no tar no smoke 0.1 0.5 0.475 0.95 0.0475. no tar smoke 0.9 0.5 0.025 0.05 0.0225. tar no smoke 0.05 0.5 0.025 0.05 0.00125. tar smoke 0.85 0.5 0.475 0.95 0.40375. Regarding the essay hills white application of Simpson’s Paradox to the Civil Rights Act and your mention of application to gender bias I would ask, how far can one go in “slicing and dicing”? How often is this an exercise in merely seeking an outcome that supports one’s pre-existing bias? For instance, can I go further and split the “north” into east and west of the Mississippi? Suppose this how the the votes came out with this further split (recall we had DemNorth(145/154), RepNorth(138/162)):
North-East: Dem(129/134 .966) North-West: Dem(16/20 = .8) Rep(109/132 .825) Now we have three regions, NorthEast, NorthWest, and sieve analysis South and analysis essay like elephants the republican % was higher in two out of three. Given the Rep(0/10) in the south that can’t be sliced in any manner to seek a favorable outcome for a rep analyst, but you get my point. I just quickly jotted down a few trials to come up with this example which is not surprising given the initial split into resume approved north-south is just a first iteration that demonstrates this is possible. But again I ask, where does the essay hills like white elephants slicing and dicing stop in such an analysis? Usually with these sorts of political and judicial analyses, those things that involve human motivations, it usually stops where the desired outcome is analysis achieved – and the best part is – one can claim it was scientific and mathematical so is indisputable! The analyst can say under oath and with a straight face,”I lay the numbers before you and the numbers don’t lie.” But just what do the numbers tell us? Your threshold “being Republican, rather than Democrat, was an important factor in causing someone to vote for the Civil Rights Act” is also subjective – as it must be in dealing with human motivations, e.g. what is ‘important’?, what is like elephants ‘causing’? One could note the 94Dem/10Rep representation from the south, and analyzing the majority of resume approved southern voter’s motivations at that time conclude that a major reason for hills like elephants the big Dem majority in that region was in part caused by the voter’s view that based on platforms and reputation, being Rep, the losing challenger was most likely in favor of the Civil Rights Act.
In see that in my previous post on “slicing and dicing” somehow things got a bit garbled between what I typed in and what displayed. One could derive the details given what did display but here is what I intended regarding the East-West split of the sieve analysis lab report North in the Civil Rights vote split: North-West Dem(16/20)=.80 Rep(109/132),825. I’ve applied Simpson’s Paradox to the North vote split. This is hypothetical, but one could gerrymander a region to analysis essay like elephants demonstrate or refute pretty much whatever one wanted. Sorry I’m a little late to the party… but I’ve been busy doing a lot of work in what I’m calling a “science of conceptual systems” where a conceptual system is a set of interrelated concepts (theories, models, mental models, policies, strategic plans, etc.). My research shows how we can use these kinds of insights to create theories and policies that are more likely to be effective in practical application.
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about one another, given , if there is a path between and where the only collider. is at . A Night All Alone. In fact, the same phenomenon can occur even in this graph: In the essay like white example you gave about the music academy, and Berkson’s paradox, there should be another node in the graph: that X gives information about three i have lived, Y if and only if X and Y have some other (external) connection. Analysis. The other connection in this case is: our intuition that music prodigies are usually disinterested in their other studies. So, you cannot proceed to the principle that when X – Z – Y, X gives information about Y, i.e. that the path is unblocked. The path is only unblocked due to the presence of another path (our personal guess that musical prodigies neglect their other studies). The immediate lesson from the new music essays dahlhaus graph of Figure B is that and can tell us something.
about essay hills like white elephants, one another, given , if there is a path between and where the only collider. is at . Schoenberg And The New Music Essays By Carl. In fact, the white elephants same phenomenon can occur even in this graph: In the resume approved example you gave about the music academy, and Berkson’s paradox, there should be another node in the graph: X gives information about Y if and only if X and Y have some other (external) connection. The other connection in this case is: our intuitive guess that music prodigies are usually disinterested in analysis elephants, their other studies. So, you cannot proceed to the principle that when X – Z Z – Y is blocked.
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Unfortunately, there are so many students that are constructing their written strongholds having no clue what kind of hills like white, things they are building (which is schoenberg and the essays, practically the same as building a house without a foundation). Nobody starts building the main part of the house and then at some point goes back to foundation; this is the hills like elephants, first thing builders work on. If we are talking about writing an three i have for essay essay, a thesis statement is a good analogy for a solid foundation. Like. The thesis statement is usually one sentence that summarizes the entire idea of the writing. Everything you choose to analysis lab report include in your essay should revolve around (be built on the foundation of) the thesis. Essay White. This is where it all should start. Prior to taking your pen or opening your new word document on your computer, you should think everything through. Just like builders know he/she should build a good foundation first, students need to know what the essay is going to be about beforehand. One has to be very careful when writing a thesis statement as it should be debatable and passions lived for essay allow for essay elephants strong evidence to be presented. Weak thesis will inevitably lead to poor essay paper outcomes just like a bad foundation will result in a ruined house.
Now having a well prepared thesis is like laying a strong foundation: when you do it right then the whole thing will stand firm. Plan. Even before laying a foundation architects have to develop a plan following which everything else is built. A blueprint is all about laying out the whole structure in advance showing how it is going to be constructed. There is no as much place for creativity when building a house if compared to the essay writing process. All creativity is to be utilized when developing a specific plan.
There are very few things that can be changed in writing essay, the process of analysis like white elephants, building as soon as the project is launched so the plan should really include all creativity. Writing an essay allows more space for creativity obviously but it doesn’t mean that the plan isn’t necessary. Quite the when a formal, opposite, an essay should also have a blueprint – an hills like white idea of how the structure of your essay is schoenberg essays, going to look like. It is usually presented in the form of statement that outlines how you are going to essay prove your thesis. It helps both the essay, writer and reader to white understand where the essay is analysis, going and hills how it is going to a modest essays end up at the final destination point. Having read your essay “blueprint” at the beginning of your document, readers will know what to expect. It will also help the writer himself/herself to organize one’s thoughts carefully. Keep in mind, this is something you work on like, prior to the writing process occurs.
Structure. Having a written blueprint and laid foundation is a good thing because it allows you to get to the building part. Now as you probably know builders don’t start from the roof or windows. There has to be the main structure built that is meant to support the entire house. All Alone. This is sort of a skeleton of the building that consists of supporting posts and beams that make up the main structure of the house.
Only after they are through this stage, the builders can move on to constructing walls, windows and roof, which if taken the anatomy analogy resemble the hills like white elephants, skin of a human body. Writing an essay again is very similar to resume approved building and this stage of like, constructing the supporting structure should be a great example of how the when writing essay, points of your essay are to analysis essay hills elephants support your thesis. And The. The points you are making in your essay are those supporting posts and rafter beams. And the stronger they are, the more solid your essay is going to be. Like the strength of analysis like, a house is tested by the winds and storms so is the points of your essay is tested by the waves of criticism and feedback. If you work hard on developing your key points then your piece of writing will weather the storm of any feedback.
Strong supporting structure have always been among the decisive factors for determining the reliability of the house. When A Formal Essay. The same principle stands for writing an essay. The entire argument depends on analysis essay hills elephants, the points you make throughout the a modest, document. A simple essay would contain 3-5 reasons why your thesis statement is analysis essay like white elephants, true. These reasons (points) are to be valid (strong) in order to make your entire essay look solid. If you did your homework and researched the topic well it won’t constitute a big problem for you to come up with those reasons. Keep in mind that literary devices are all good and they help to make your essay better but without having a blueprint, foundation, and when a formal good supporting structure they don’t do any good at all. Those nice words and complex devices are like beautiful building color that doesn’t really matter when it all falls apart.
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Rajendra Prasad was. Constitution , Constitution of India , Government of India 1152 Words | 4 Pages. ?1. FRENCH AND INDIAN WAR (1754–1763) The French and Indian War (1754–1763) was the analysis essay hills like last of a series of great colonial wars that . stretched for almost a hundred years and disrupted settlements throughout North America. It marked the end of the a modest proposal essays French empire in North America and the beginning of English domination of the continent.
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Sherman Alexie , The Absolutely True Diary of analysis elephants, a Part-Time Indian , The Beautiful Life 1007 Words | 3 Pages. has failed for especially the weaker parts of Indian society ie agricultural labourers, marginal and proposal, small farmers . It already . Analysis Hills White Elephants! boasts one of the highest unemployment rates, and despite its agricultural success, farmers livelihoods have been declining resulting in a record number of farmer suicides. The various reasons, for a formal essay suicides among Punjab farmers is perturbing enough to essay hills like white warrant a serious study. In the present case, suicide among Punjab farmers have by all means become a public issue as these. Suicide , The Complete Manual of proposal essays, Suicide 2382 Words | 7 Pages. ?Critical Thinking Essay For thousands of years, Indians freely inhabited American land with peace and harmony. Then, all of . Analysis Hills White Elephants! that drastically changed when the white settlers began encroaching on their territory. A Modest Proposal! Only the Five Civilized Tribes by the 1830's proved to be the like elephants most suitable in this rapidly changing environment, but just when they started adopting the whites' ways of life, they were forced out of schoenberg and the new music by carl dahlhaus, their land. Years have passed and Indians still only hills like white hold small pieces of territory. Although. Andrew Jackson , Cherokee , Chickasaw 897 Words | 3 Pages.
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Sanjay B. Kadu, Vidya Bharti Mahavidyalaya, Camp, Amravati. . [email protected] [email protected] Mobile : 9420189295 ____________________________________________________________________________________________ India is an agricultural country; one third population depends on agriculture sector directly or indirectly. Agriculture continues to be the mainstays. Agricultural policy , Agricultural science , Agriculture 1344 Words | 5 Pages. Indian Suffrage Before the English arrived in the New world and began creating colonies, the American Indians lived in harmony . and peace with natures. The American Indians were skilled hunters, farmers and used everything in their environment for survival or for when writing essay essential necessities. They shared the land together and essay, moved about freely in search of food. The American Indians never considered the lands their property because it's belong to resume approved God and analysis hills white elephants, no one have the right to buy, sell, nor own. Dawes Act , Genocide , Indian 1474 Words | 4 Pages. The Anasazi Indians were a very interesting tribe. The word Anasazi is a Navajo word meaning Ancient Ones.
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However, it is evident that the Economic crisis was the main reason for the increased electoral support. Adolf Hitler , Germany , Great Depression 1353 Words | 4 Pages. banks of the Indian river Ganges in the sixth millennium BC. So were species of winter cereals (barley, oats, and wheat) and legumes (lentil . and chickpea) grown in essay hills like white elephants, Northwest India before the sixth millennium BC. Other crops cultivated in India 3000 to 6000 years ago, include sesame, linseed, safflower, mustards, castor, mung bean, black gram, horse gram, pigeonpea, field pea, grass pea (khesari), fenugreek, cotton, jujube, grapes, dates, jackfruit, mango, mulberry, and black plum. Indian peasants had. Agriculture , Civilization , Economics 884 Words | 3 Pages. Mark Amariyakoune April 22, 2013 ENG 101 Essay 1 Paul Farmer : Man On A Mission How far will one man go to resume approved achieve the . Essay Hills White Elephants! impossible? How far can one man go to reach his goal? The country of Haiti is one of the essays most under developed countries in the world, but one doctor, Paul Farmer , is determined to help cure this country.
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A question (“Why did . communism collapse in Eastern Europe?”) is not an argument, and without an argument, a thesis is proposal dead in essay white, the water. 2. A thesis is never a list. “For political, economic, social and cultural reasons, communism collapsed in Eastern Europe” does a good job of “telegraphing” the when writing a formal essay reader what to expect in the essay —a section about political reasons, a section about. Argument , Frederick Douglass , Logic 1094 Words | 5 Pages. knows that the analysis white Native American Indians have been around for a long time, some more than others. When Writing A Formal Essay! The Native American Indians were . known to have separated into different groups or tribes. Eventually each tribe began to speak their own language and hills elephants, started doing things that differentiated them from the rest of the tribes. Essay! Two of the most important tribes were the Iroquois and Pueblo tribes. The Iroquois Indians , believed to be the most influential of essay hills white elephants, all the Indians , lived in the areas of essay, Ontario. Indigenous peoples of the Americas , Iroquois , Native Americans in the United States 512 Words | 2 Pages.
that there was no centralized empire until much later. Elephants! Many important social and cultural aspects of resume approved, Indian society outlived the Gupta . rule in the classical era. Hinduism was supported by the Gupta emperors over Buddhism because Buddhism gradually declined and spread beyond India to different places. So Hinduism remained as the highly dominate religion. This symbolizes that the Indian society remained together by its common Hindu religion traits. Math and Science was also signified by the.
Buddhism , Hindu , Hinduism 487 Words | 2 Pages. Felippe Wancelotti Mrs. Amelkin AP Lang 10/4/2012 “ Indian Education” Subject: Sherman Alexie delivers an essay portraying . his life from a yearly view-point encompassing the 1st to 12th grade. Like! Occasion: Indian misconceptions, mistreatments, stereotypes, and discriminations all affected Alexie on his educational highway and for essay, served as a basis for the writing of analysis hills like white elephants, “ Indian Education”. Audience: Alexie’s audience is primarily those interested in the lifestyle of Native Americans. Purpose: Alexie. Caribbean , Discrimination , Educational years 769 Words | 3 Pages. 9/24/2010 Cahokia Essay As Indian groups started to settle in the Mississippi floodplain, their cultures and political systems . began to resume approved intertwine, creating a complex sociopolitical structure (Page, 70). Analysis Essay Like White Elephants! The largest polity to arise out of this area, known as the American Bottom, was Cahokia. At its height, it resembled a city, extending over five square miles, mounds and structures that towered over smaller dwellings, and a population, that some believe to have been the largest, north of Mexico.
Economics , Economy , Elite 843 Words | 3 Pages. tiny hamlets of thatched huts to larger settlements of tile-roofed stone and brick houses. Most Indian villages are small; nearly 80 percent . Three Passions Lived! have fewer than 1,000 inhabitants, according to the 1991 census. Essay Like White Elephants! Most are nucleated settlements, while others are more dispersed. Resume Approved! It is in villages that India's most basic business--agriculture--takes place. Here, in the face of vicissitudes of essay hills white elephants, all kinds, farmers follow time-tested as well as innovative methods of a formal essay, growing wheat, rice, lentils, vegetables, fruits. Caste system in India , City , Dispersed settlement 961 Words | 3 Pages. Peasantry: Caribbean and Small Farmers. What is essay hills like Peasantry? Peasant farming is sieve analysis lab report described as small-scale farming for subsistence as well as for cash sale in the market.
Initially, small . farmers in the British West Indies produced crops for domestic use as well as for sale in like elephants, the market. However, after 1860 these farmers began to a night essay export their crop. Reasons for the development of alternative crops 1. After 1834, small-scale agriculture grew out of the free-village movement as free blacks were determined to leave the white elephants sugar estate. Ex-slaves. Agriculture , Barbados , British Empire 861 Words | 3 Pages. Impact of FDI In The Indian Retail Sector By: Aditi Mehta 12/PPRA/504 Foreign Direct Investment (FDI) FDI is a mode of entry to . international business. Three For Essay! It refers to essay white the investment made in a foreign country where the investor retains control over the investments. Proposal! This can be made by an individual, as well as by business entities.
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Racism and. Education , High school , Indigenous peoples of the Americas 998 Words | 3 Pages. class, how did Indians respond to the government’s agenda to essay hills like solve “the Indian Problem”? Where did they cooperate—and why—and . where did they resist—and why? The “ Indian Problem” was the “burden” that the United States Government faced throughout the 19th and early 20th centuries. The Government considered the Indians to be a “problem” due to the fact that native tribes were halting the expansionist policy popular in the 1800’s. The main aspects targeted and defined as the “ Indian Problem” by.
Federal government of the United States , Hawaii , Hopi 2171 Words | 6 Pages. Most Indian cuisine are related by the similar usage of spices and the use of a greater variety of vegetables than many other cuisine. . Religious and a night essay, caste restrictions, weather, geography and the impact of foreigners have affected the eating habits of Indians . For example, Brahmins (one of the highest orders of caste) are strict vegetarians usually, but in the coastal states of West Bengal and Kerala, they consume a lot of fish. Southern Indians generally speaking, have been orthodox in analysis like elephants, their tastes. Curry , Idli , India 1499 Words | 4 Pages. purchased an earlier edition of the Parrillo text, be advised that the material will in places be on different pages from the 9th edition and you are . responsible for the material as it appears in the 9th Edition. Raymond Krech. The Ecological Indian . The Ecological Indian Book Review: For this assignment you will be required to answer five questions (20 points each) and integrate concepts, theories and ideas from your textbook (chapters 1-4) that help explain the issues you encounter in this book.
Provide. Allyn Bacon , Amerigo Vespucci , Answer 805 Words | 3 Pages. the One Malaysia campaign and as a good citizen,we must instil a good attitude from home so that we can apply it at school.The form teacher has to plan a . proper seating arrangement by analysis lab report combining different races of students such as Malay,Chinese, Indians and others to bulid strong relationship and tolerance among students.We should have sufficient tables and chairs in class and make sure they are safe to analysis essay like white be used.Make report to the respective teacher about the broken furniture in class immediately. Classroom , Education , Learning 796 Words | 3 Pages. ?Beginning Farmers and Ranchers A financially viable farm business can require control of substantial assets, posing a major obstacle to . potential new farmers or ranchers. Several U.S. Department of Agriculture (USDA) programs are designed to support the special needs of beginning farmers and ranchers, including financial support in the form of loans and higher conservation payment rates. What Is the schoenberg dahlhaus Issue? Policymakers have responded to essay hills like white elephants the perceived needs of beginning farmers and ranchers.
Agriculture , Farm , Household 856 Words | 2 Pages. railroads to charge what they wanted. Railroads were the only way for many western farmers to get their produce to market and high prices were . always charged. Railroads controlled storage, elevators, and warehouses so the and the new music essays by carl prices the farmers paid were very high. Middlemen- Middlemen set the price of the produce low when they sold because the essay hills market price was unpredictable. Bankers- High interest rates caused the farmers to pay even more when they didn't have the money to pay.
Trusts- Trusts such. Agriculture , Bank , Crop 624 Words | 3 Pages. Indian Art is the art produced on the Indian subcontinent from about the 3rd millennium BC to modern times. To viewers schooled . in a modest proposal essays, the Western tradition, Indian art may seem overly ornate and like elephants, sensuous; appreciation of its refinement comes only resume approved gradually, as a rule. Hills Like! Voluptuous feeling is given unusually free expression in Indian culture. Analysis Lab Report! A strong sense of design is also characteristic of Indian art and can be observed in its modern as well as in its traditional forms. The vast scope of the art of. Ajanta Caves , Art , India 2253 Words | 7 Pages.
Surya Shrestha KAS Mr. Ganga Sagar Mepu Farmer 9841712815 Mr. Ram Prasad Timalsina Farmer 9849634637 Mr. Raj Kumar . Essay Hills Like! Subedi Farmer 9841576392 Ms. Roja Rijal Farmer 9843056475 Ms. Nirmala Timilsina Farmer 9841185401 Ms. A Night All Alone! Bhagawati Poudel Farmer Ms. Danda Kumari Thapa Farmer Ms.
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