andrew_gelman_stats andrew_gelman_stats-2014 andrew_gelman_stats-2014-2182 knowledge-graph by maker-knowledge-mining
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Introduction: One of the new examples for the third edition of Bayesian Data Analysis is a spell-checking story. Here it is (just start at 2/3 down on the first page, with “Spelling correction”). I like this example—it demonstrates the Bayesian algebra, also gives a sense of the way that probability models (both “likelihood” and “prior”) are constructed from existing assumptions and data. The models aren’t just specified as a mathematical exercise, they represent some statement about reality. And the problem is close enough to our experience that we can consider ways in which the model can be criticized and improved, all in a simple example that has only three possibilities.
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Introduction: One of the new examples for the third edition of Bayesian Data Analysis is a spell-checking story. Here it is (just start at 2/3 down on the first page, with “Spelling correction”). I like this example—it demonstrates the Bayesian algebra, also gives a sense of the way that probability models (both “likelihood” and “prior”) are constructed from existing assumptions and data. The models aren’t just specified as a mathematical exercise, they represent some statement about reality. And the problem is close enough to our experience that we can consider ways in which the model can be criticized and improved, all in a simple example that has only three possibilities.
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Introduction: I’ve been writing a lot about my philosophy of Bayesian statistics and how it fits into Popper’s ideas about falsification and Kuhn’s ideas about scientific revolutions. Here’s my long, somewhat technical paper with Cosma Shalizi. Here’s our shorter overview for the volume on the philosophy of social science. Here’s my latest try (for an online symposium), focusing on the key issues. I’m pretty happy with my approach–the familiar idea that Bayesian data analysis iterates the three steps of model building, inference, and model checking–but it does have some unresolved (maybe unresolvable) problems. Here are a couple mentioned in the third of the above links. Consider a simple model with independent data y_1, y_2, .., y_10 ~ N(θ,σ^2), with a prior distribution θ ~ N(0,10^2) and σ known and taking on some value of approximately 10. Inference about μ is straightforward, as is model checking, whether based on graphs or numerical summaries such as the sample variance and skewn
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Introduction: I received the following email: I have an interesting thought on a prior for a logistic regression, and would love your input on how to make it “work.” Some of my research, two published papers, are on mathematical models of **. Along those lines, I’m interested in developing more models for **. . . . Empirical studies show that the public is rather smart and that the wisdom-of-the-crowd is fairly accurate. So, my thought would be to tread the public’s probability of the event as a prior, and then see how adding data, through a model, would change or perturb our inferred probability of **. (Similarly, I could envision using previously published epidemiological research as a prior probability of a disease, and then seeing how the addition of new testing protocols would update that belief.) However, everything I learned about hierarchical Bayesian models has a prior as a distribution on the coefficients. I don’t know how to start with a prior point estimate for the probabili
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Introduction: This post is by Phil Price. The New York Times recently ran an article entitled “How Exercise Can Help Us Eat Less,” which begins with this: “Strenuous exercise seems to dull the urge to eat afterward better than gentler workouts, several new studies show, adding to a growing body of science suggesting that intense exercise may have unique benefits.” The article is based on a couple of recent studies in which moderately overweight volunteers participated in different types of exercise, and had their food intake monitored at a subsequent meal. The article also says “[The volunteers] also displayed significantly lower levels of the hormone ghrelin, which is known to stimulate appetite, and elevated levels of both blood lactate and blood sugar, which have been shown to lessen the drive to eat, after the most vigorous interval session than after the other workouts. And the appetite-suppressing effect of the highly intense intervals lingered into the next day, according to food diarie
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Introduction: Bayesian inference, conditional on the model and data, conforms to the likelihood principle. But there is more to Bayesian methods than Bayesian inference. See chapters 6 and 7 of Bayesian Data Analysis for much discussion of this point. It saddens me to see that people are still confused on this issue.
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Introduction: One of the new examples for the third edition of Bayesian Data Analysis is a spell-checking story. Here it is (just start at 2/3 down on the first page, with “Spelling correction”). I like this example—it demonstrates the Bayesian algebra, also gives a sense of the way that probability models (both “likelihood” and “prior”) are constructed from existing assumptions and data. The models aren’t just specified as a mathematical exercise, they represent some statement about reality. And the problem is close enough to our experience that we can consider ways in which the model can be criticized and improved, all in a simple example that has only three possibilities.
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Introduction: Ryan Ickert writes: I was wondering if you’d seen this post , by a particle physicist with some degree of influence. Dr. Dorigo works at CERN and Fermilab. The penultimate paragraph is: From the above expression, the Frequentist researcher concludes that the tracker is indeed biased, and rejects the null hypothesis H0, since there is a less-than-2% probability (P’<α) that a result as the one observed could arise by chance! A Frequentist thus draws, strongly, the opposite conclusion than a Bayesian from the same set of data. How to solve the riddle? He goes on to not solve the riddle. Perhaps you can? Surely with the large sample size they have (n=10^6), the precision on the frequentist p-value is pretty good, is it not? My reply: The first comment on the site (by Anonymous [who, just to be clear, is not me; I have no idea who wrote that comment], 22 Feb 2012, 21:27pm) pretty much nails it: In setting up the Bayesian model, Dorigo assumed a silly distribution on th
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Introduction: Astrophysicist Andrew Jaffe pointed me to this and discussion of my philosophy of statistics (which is, in turn, my rational reconstruction of the statistical practice of Bayesians such as Rubin and Jaynes). Jaffe’s summary is fair enough and I only disagree in a few points: 1. Jaffe writes: Subjective probability, at least the way it is actually used by practicing scientists, is a sort of “as-if” subjectivity — how would an agent reason if her beliefs were reflected in a certain set of probability distributions? This is why when I discuss probability I try to make the pedantic point that all probabilities are conditional, at least on some background prior information or context. I agree, and my problem with the usual procedures used for Bayesian model comparison and Bayesian model averaging is not that these approaches are subjective but that the particular models being considered don’t make sense. I’m thinking of the sorts of models that say the truth is either A or
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Introduction: Deborah Mayo pointed me to this discussion by Christian Hennig of my recent article on Induction and Deduction in Bayesian Data Analysis. A couple days ago I responded to comments by Mayo, Stephen Senn, and Larry Wasserman. I will respond to Hennig by pulling out paragraphs from his discussion and then replying. Hennig: for me the terms “frequentist” and “subjective Bayes” point to interpretations of probability, and not to specific methods of inference. The frequentist one refers to the idea that there is an underlying data generating process that repeatedly throws out data and would approximate the assumed distribution if one could only repeat it infinitely often. Hennig makes the good point that, if this is the way you would define “frequentist” (it’s not how I’d define the term myself, but I’ll use Hennig’s definition here), then it makes sense to be a frequentist in some settings but not others. Dice really can be rolled over and over again; a sample survey of 15
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Introduction: I’ve been writing a lot about my philosophy of Bayesian statistics and how it fits into Popper’s ideas about falsification and Kuhn’s ideas about scientific revolutions. Here’s my long, somewhat technical paper with Cosma Shalizi. Here’s our shorter overview for the volume on the philosophy of social science. Here’s my latest try (for an online symposium), focusing on the key issues. I’m pretty happy with my approach–the familiar idea that Bayesian data analysis iterates the three steps of model building, inference, and model checking–but it does have some unresolved (maybe unresolvable) problems. Here are a couple mentioned in the third of the above links. Consider a simple model with independent data y_1, y_2, .., y_10 ~ N(θ,σ^2), with a prior distribution θ ~ N(0,10^2) and σ known and taking on some value of approximately 10. Inference about μ is straightforward, as is model checking, whether based on graphs or numerical summaries such as the sample variance and skewn
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Introduction: Tyler Cowen asks the above question. I don’t have a full answer, but, in the Economics section of A Quantitative Tour of the Social Sciences , Richard Clarida discusses in detail the ways that researchers have tried to estimate the extent to which government or private forecasts supply additional information.
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Introduction: One of the new examples for the third edition of Bayesian Data Analysis is a spell-checking story. Here it is (just start at 2/3 down on the first page, with “Spelling correction”). I like this example—it demonstrates the Bayesian algebra, also gives a sense of the way that probability models (both “likelihood” and “prior”) are constructed from existing assumptions and data. The models aren’t just specified as a mathematical exercise, they represent some statement about reality. And the problem is close enough to our experience that we can consider ways in which the model can be criticized and improved, all in a simple example that has only three possibilities.
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Introduction: In an article provocatively entitled, “Will Ohio State’s football team decide who wins the White House?”, Tyler Cowen and Kevin Grier report : It is statistically possible that the outcome of a handful of college football games in the right battleground states could determine the race for the White House. Economists Andrew Healy, Neil Malhotra, and Cecilia Mo make this argument in a fascinating article in the Proceedings of the National Academy of Science. They examined whether the outcomes of college football games on the eve of elections for presidents, senators, and governors affected the choices voters made. They found that a win by the local team, in the week before an election, raises the vote going to the incumbent by around 1.5 percentage points. When it comes to the 20 highest attendance teams—big athletic programs like the University of Michigan, Oklahoma, and Southern Cal—a victory on the eve of an election pushes the vote for the incumbent up by 3 percentage points. T
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Introduction: As a statistician I am particularly worried about the rhetorical power of anecdotes (even though I use them in my own reasoning; see discussion below). But much can be learned from a true anecdote. The rough edges—the places where the anecdote doesn’t fit your thesis—these are where you learn. We have recently had a discussion ( here and here ) of Karl Weick, a prominent scholar of business management who plagiarized a story and then went on to draw different lessons from the pilfered anecdote in several different publications published over many years. Setting aside an issues of plagiarism and rulebreaking, I argue that, by hiding the source of the story and changing its form, Weick and his management-science audience are losing their ability to get anything out of it beyond empty confirmation. A full discussion follows. 1. The lost Hungarian soldiers Thomas Basbøll (who has the unusual (to me) job of “writing consultant” at the Copenhagen Business School) has been
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