andrew_gelman_stats andrew_gelman_stats-2011 andrew_gelman_stats-2011-998 knowledge-graph by maker-knowledge-mining
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Introduction: Sean O’Riordain writes: Your article, “ The holes in my philosophy of Bayesian data analysis ” caused me to wonder whether it was possible to have a consistent philosophy of data analysis and whether it could it be possible that Godel’s incompleteness theorem extends as far as to say that it wasn’t possible? I don’t know but my guess is that this is all related to our lack of a good model for hypothesis generation. Statistics focuses on deductive inference within models and model checking to evaluate models, but we don’t have a good handle on the creation of models. (I’m hoping that some of our network-of-models stuff will be helpful.)
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1 I don’t know but my guess is that this is all related to our lack of a good model for hypothesis generation. [sent-2, score-0.754]
2 Statistics focuses on deductive inference within models and model checking to evaluate models, but we don’t have a good handle on the creation of models. [sent-3, score-1.755]
3 (I’m hoping that some of our network-of-models stuff will be helpful. [sent-4, score-0.292]
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Introduction: Sean O’Riordain writes: Your article, “ The holes in my philosophy of Bayesian data analysis ” caused me to wonder whether it was possible to have a consistent philosophy of data analysis and whether it could it be possible that Godel’s incompleteness theorem extends as far as to say that it wasn’t possible? I don’t know but my guess is that this is all related to our lack of a good model for hypothesis generation. Statistics focuses on deductive inference within models and model checking to evaluate models, but we don’t have a good handle on the creation of models. (I’m hoping that some of our network-of-models stuff will be helpful.)
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Introduction: Here’s an article that I believe is flat-out entertaining to read. It’s about philosophy, so it’s supposed to be entertaining, in any case. Here’s the abstract: A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually support that particular philosophy but rather accord much better with sophisticated forms of hypothetico-deductivism. We examine the actual role played by prior distributions in Bayesian models, and the crucial aspects of model checking and model revision, which fall outside the scope of Bayesian confirmation theory. We draw on the literature on the consistency of Bayesian updating and also on our experience of applied work in social science. Clarity about these matters should benefit not just philosophy of science, but
3 0.23867801 1719 andrew gelman stats-2013-02-11-Why waste time philosophizing?
Introduction: I’ll answer the above question after first sharing some background and history on the the philosophy of Bayesian statistics, which appeared at the end of our rejoinder to the discussion to which I linked the other day: When we were beginning our statistical educations, the word ‘Bayesian’ conveyed membership in an obscure cult. Statisticians who were outside the charmed circle could ignore the Bayesian subfield, while Bayesians themselves tended to be either apologetic or brazenly defiant. These two extremes manifested themselves in ever more elaborate proposals for non-informative priors, on the one hand, and declarations of the purity of subjective probability, on the other. Much has changed in the past 30 years. ‘Bayesian’ is now often used in casual scientific parlance as a synonym for ‘rational’, the anti-Bayesians have mostly disappeared, and non-Bayesian statisticians feel the need to keep up with developments in Bayesian modelling and computation. Bayesians themselves
4 0.21431981 746 andrew gelman stats-2011-06-05-An unexpected benefit of Arrow’s other theorem
Introduction: In my remarks on Arrow’s theorem (the weak form of Arrow’s Theorem is that any result can be published no more than five times. The strong form is that every result will be published five times), I meant no criticism of Bruno Frey, the author of the articles in question: I agree that it can be a contribution to publish in multiple places. Regarding the evaluation of contributions, it should be possible to evaluate research contributions and also evaluate communication. One problem is that communication is both under- and over-counted. It’s undercounted in that we mostly get credit for original ideas not for exposition; it’s overcounted in that we need communication skills to publish in the top journals. But I don’t think these two biases cancel out. The real reason I’m bringing this up, though, is because Arrow’s theorem happened to me recently and in interesting way. Here’s the story. Two years ago I was contacted by Harold Kincaid to write a chapter on Bayesian statistics
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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: Sean O’Riordain writes: Your article, “ The holes in my philosophy of Bayesian data analysis ” caused me to wonder whether it was possible to have a consistent philosophy of data analysis and whether it could it be possible that Godel’s incompleteness theorem extends as far as to say that it wasn’t possible? I don’t know but my guess is that this is all related to our lack of a good model for hypothesis generation. Statistics focuses on deductive inference within models and model checking to evaluate models, but we don’t have a good handle on the creation of models. (I’m hoping that some of our network-of-models stuff will be helpful.)
2 0.81966221 904 andrew gelman stats-2011-09-13-My wikipedia edit
Introduction: The other day someone mentioned my complaint about the Wikipedia article on “Bayesian inference” (see footnote 1 of this article ) and he said I should fix the Wikipedia entry myself. And so I did . I didn’t have the energy to rewrite the whole article–in particular, all of its examples involve discrete parameters, whereas the Bayesian problems I work on generally have continuous parameters, and its “mathematical foundations” section focuses on “independent identically distributed observations x” rather than data y which can have different distributions. It’s just a wacky, unbalanced article. But I altered the first few paragraphs to get rid of the stuff about the posterior probability that a model is true. I much prefer the Scholarpedia article on Bayesian statistics by David Spiegelhalter and Kenneth Rice, but I couldn’t bring myself to simply delete the Wikipedia article and replace it with the Scholarpedia content. Just to be clear: I’m not at all trying to disparage
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Introduction: I’ll answer the above question after first sharing some background and history on the the philosophy of Bayesian statistics, which appeared at the end of our rejoinder to the discussion to which I linked the other day: When we were beginning our statistical educations, the word ‘Bayesian’ conveyed membership in an obscure cult. Statisticians who were outside the charmed circle could ignore the Bayesian subfield, while Bayesians themselves tended to be either apologetic or brazenly defiant. These two extremes manifested themselves in ever more elaborate proposals for non-informative priors, on the one hand, and declarations of the purity of subjective probability, on the other. Much has changed in the past 30 years. ‘Bayesian’ is now often used in casual scientific parlance as a synonym for ‘rational’, the anti-Bayesians have mostly disappeared, and non-Bayesian statisticians feel the need to keep up with developments in Bayesian modelling and computation. Bayesians themselves
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Introduction: Deborah Mayo collected some reactions to my recent article , Induction and Deduction in Bayesian Data Analysis. I’m pleased that that everybody (philosopher Mayo, applied statistician Stephen Senn, and theoretical statistician Larry Wasserman) is so positive about my article and that nobody’s defending the sort of hard-core inductivism that’s featured on the Bayesian inference wikipedia page. Here’s the Wikipedia definition, which I disagree with: Bayesian inference uses aspects of the scientific method, which involves collecting evidence that is meant to be consistent or inconsistent with a given hypothesis. As evidence accumulates, the degree of belief in a hypothesis ought to change. With enough evidence, it should become very high or very low. . . . Bayesian inference uses a numerical estimate of the degree of belief in a hypothesis before evidence has been observed and calculates a numerical estimate of the degree of belief in the hypothesis after evidence has been obse
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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: Anna Lena Phillips writes : I. Many people will not, of their own accord, look at a poem. II. Millions of people will, of their own accord, spend lots and lots of time looking at photographs of cats. III. Therefore, earlier this year, I concluded that the best strategy for increasing the number of viewers for poems would be to print them on top of photographs of cats. IV. I happen to like looking at both poems and cats. V. So this is, for me, a win-win situation. VI. Fortunately, my own cat is a patient model, and (if I am to be believed) quite photogenic. VII. The aforementioned cat is Tisko Tansi, small hero. VII. Thus I present to you (albeit in digital rather than physical form) an Endearments broadside, featuring a poem that originally appeared in BlazeVOX spring 2011. VIII. If you want to share a copy of this image, please ask first. If you want a real copy, you can ask about that too. She follows up with an image of a cat, on which is superimposed a short
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Introduction: I saw this picture staring at me from the newsstand the other day: Here’s the accompanying article, by Michael Scherer and Michael Duffy, which echoes some of the points I made a few months ago , following the midterm election: Why didn’t Obama do a better job of leveling with the American people? In his first months in office, why didn’t he anticipate the example of the incoming British government and warn people of economic blood, sweat, and tears? Why did his economic team release overly-optimistic graphs such as shown here? Wouldn’t it have been better to have set low expectations and then exceed them, rather than the reverse? I don’t know, but here’s my theory. When Obama came into office, I imagine one of his major goals was to avoid repeating the experiences of Bill Clinton and Jimmy Carter in their first two years. Clinton, you may recall, was elected with less then 50% of the vote, was never given the respect of a “mandate” by congressional Republicans, wasted
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Introduction: Sean O’Riordain writes: Your article, “ The holes in my philosophy of Bayesian data analysis ” caused me to wonder whether it was possible to have a consistent philosophy of data analysis and whether it could it be possible that Godel’s incompleteness theorem extends as far as to say that it wasn’t possible? I don’t know but my guess is that this is all related to our lack of a good model for hypothesis generation. Statistics focuses on deductive inference within models and model checking to evaluate models, but we don’t have a good handle on the creation of models. (I’m hoping that some of our network-of-models stuff will be helpful.)
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Introduction: Derek Sonderegger writes: I have just finished my Ph.D. in statistics and am currently working in applied statistics (plant ecology) using Bayesian statistics. As the statistician in the group I only ever get the ‘hard analysis’ problems that don’t readily fit into standard models. As I delve into the computational aspects of Bayesian analysis, I find myself increasingly frustrated with the current set of tools. I was delighted to see JAGS 2.0 just came out and spent yesterday happily playing with it. My question is, where do you see the short-term future of Bayesian computing going and what can we do to steer it in a particular direction? In your book with Dr Hill, you mention that you expect BUGS (or its successor) to become increasingly sophisticated and, for example, re-parameterizations that increase convergence rates would be handled automatically. Just as R has been successful because users can extend it, I think progress here also will be made by input from ‘p
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