andrew_gelman_stats andrew_gelman_stats-2012 andrew_gelman_stats-2012-1151 knowledge-graph by maker-knowledge-mining
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Introduction: Continuing with my discussion of the articles in the special issue of the journal Rationality, Markets and Morals on the philosophy of Bayesian statistics: Stephen Senn, “You May Believe You Are a Bayesian But You Are Probably Wrong”: I agree with Senn’s comments on the impossibility of the de Finetti subjective Bayesian approach. As I wrote in 2008, if you could really construct a subjective prior you believe in, why not just look at the data and write down your subjective posterior. The immense practical difficulties with any serious system of inference render it absurd to think that it would be possible to just write down a probability distribution to represent uncertainty. I wish, however, that Senn would recognize my Bayesian approach (which is also that of John Carlin, Hal Stern, Don Rubin, and, I believe, others). De Finetti is no longer around, but we are! I have to admit that my own Bayesian views and practices have changed. In particular, I resonate wit
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1 As I wrote in 2008, if you could really construct a subjective prior you believe in, why not just look at the data and write down your subjective posterior. [sent-2, score-1.0]
2 The immense practical difficulties with any serious system of inference render it absurd to think that it would be possible to just write down a probability distribution to represent uncertainty. [sent-3, score-0.68]
3 I have to admit that my own Bayesian views and practices have changed. [sent-6, score-0.076]
4 In particular, I resonate with Senn’s point that conventional flat priors miss a lot and that Bayesian inference can work better when real prior information is used. [sent-7, score-0.639]
5 Here I’m not talking about a subjective prior that is meant to express a personal belief but rather a distribution that represents a summary of prior scientific knowledge. [sent-8, score-0.979]
6 Such an expression can only be approximate (as, indeed, assumptions such as logistic regressions, additive treatment effects, and all the rest, are only approximations too), and I agree with Senn that it would be rash to let philosophical foundations be a justification for using Bayesian methods. [sent-9, score-0.726]
7 Rather, my work on the philosophy of statistics is intended to demonstrate how Bayesian inference can fit into a falsificationist philosophy that I am comfortable with on general grounds. [sent-10, score-0.806]
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Introduction: Continuing with my discussion of the articles in the special issue of the journal Rationality, Markets and Morals on the philosophy of Bayesian statistics: Stephen Senn, “You May Believe You Are a Bayesian But You Are Probably Wrong”: I agree with Senn’s comments on the impossibility of the de Finetti subjective Bayesian approach. As I wrote in 2008, if you could really construct a subjective prior you believe in, why not just look at the data and write down your subjective posterior. The immense practical difficulties with any serious system of inference render it absurd to think that it would be possible to just write down a probability distribution to represent uncertainty. I wish, however, that Senn would recognize my Bayesian approach (which is also that of John Carlin, Hal Stern, Don Rubin, and, I believe, others). De Finetti is no longer around, but we are! I have to admit that my own Bayesian views and practices have changed. In particular, I resonate wit
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Introduction: I recently saw this article that Stephen Senn wrote a couple of years ago, criticizing Bayesian sensitivity analyses that relied on vague prior distributions. I’m moving more and more toward the idea that Bayesian analysis should include actual prior information, so I generally agree with his points. As I used to say when teaching Bayesian data analysis, a Bayesian model is modular, and different pieces can be swapped in and out as needed. So you might start with an extremely weak prior distribution, but if it makes a difference it’s time to bite the bullet and include more information. My only disagreement with Senn’s paper is in its recommendation to try the so-called fixed-effects analysis. Beyond the difficulties with terminology (the expressions “fixed” and “random” effects are defined in different ways by different people in the literature; see here for a rant on the topic which made its way into some of my articles and books), there is the problem that, when a model ge
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Introduction: Some recent blog discussion revealed some confusion that I’ll try to resolve here. I wrote that I’m not a big fan of subjective priors. Various commenters had difficulty with this point, and I think the issue was most clearly stated by Bill Jeff re erys, who wrote : It seems to me that your prior has to reflect your subjective information before you look at the data. How can it not? But this does not mean that the (subjective) prior that you choose is irrefutable; Surely a prior that reflects prior information just does not have to be inconsistent with that information. But that still leaves a range of priors that are consistent with it, the sort of priors that one would use in a sensitivity analysis, for example. I think I see what Bill is getting at. A prior represents your subjective belief, or some approximation to your subjective belief, even if it’s not perfect. That sounds reasonable but I don’t think it works. Or, at least, it often doesn’t work. Let’s start
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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: Continuing with my discussion of the articles in the special issue of the journal Rationality, Markets and Morals on the philosophy of Bayesian statistics: Stephen Senn, “You May Believe You Are a Bayesian But You Are Probably Wrong”: I agree with Senn’s comments on the impossibility of the de Finetti subjective Bayesian approach. As I wrote in 2008, if you could really construct a subjective prior you believe in, why not just look at the data and write down your subjective posterior. The immense practical difficulties with any serious system of inference render it absurd to think that it would be possible to just write down a probability distribution to represent uncertainty. I wish, however, that Senn would recognize my Bayesian approach (which is also that of John Carlin, Hal Stern, Don Rubin, and, I believe, others). De Finetti is no longer around, but we are! I have to admit that my own Bayesian views and practices have changed. In particular, I resonate wit
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Introduction: Charlie Williams writes: As I get interested in Bayesian approaches to statistics, I have one question I wondered if you would find interesting to address at some point on the blog. What does Bayesian work look like in action across a field? From experience, I have some feeling for how ongoing debates evolve (or not) with subsequent studies in response to earlier findings. I wonder if you know how this happens in practice when multiple researchers are using Bayesian approaches. How much are previous findings built into priors? How much advance comes from model improvement? And in a social science field where self-selection and self-interest play a role, how are improved “treatment” effects incorporated and evaluated? I thought you might know of a field where actual back and forth has been carried out mostly in the context of Bayesian analysis or inference, and I thought it would be interesting to take a look at an example as I think about my own field. My reply: I’ve seen Ba
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Introduction: Continuing with my discussion here and here of the articles in the special issue of the journal Rationality, Markets and Morals on the philosophy of Bayesian statistics: David Hendry, “Empirical Economic Model Discovery and Theory Evaluation”: Hendry presents a wide-ranging overview of scientific learning, with an interesting comparison of physical with social sciences. (For some reason, he discusses many physical sciences but restricts his social-science examples to economics and psychology.) The only part of Hendry’s long and interesting article that I will discuss, however, is the part where he decides to take a gratuitous swing at Bayes. I don’t know why he did this, but maybe it’s part of some fraternity initiation thing, like TP-ing the dean’s house on Halloween. Here’s the story. Hendry writes: ‘Prior distributions’ widely used in Bayesian analyses, whether subjective or ‘objective’, cannot be formed in such a setting either, absent a falsely assumed crys
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Introduction: Continuing with my discussion of the articles in the special issue of the journal Rationality, Markets and Morals on the philosophy of Bayesian statistics: Stephen Senn, “You May Believe You Are a Bayesian But You Are Probably Wrong”: I agree with Senn’s comments on the impossibility of the de Finetti subjective Bayesian approach. As I wrote in 2008, if you could really construct a subjective prior you believe in, why not just look at the data and write down your subjective posterior. The immense practical difficulties with any serious system of inference render it absurd to think that it would be possible to just write down a probability distribution to represent uncertainty. I wish, however, that Senn would recognize my Bayesian approach (which is also that of John Carlin, Hal Stern, Don Rubin, and, I believe, others). De Finetti is no longer around, but we are! I have to admit that my own Bayesian views and practices have changed. In particular, I resonate wit
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Introduction: What we did in our Stan meeting yesterday: Some discussion of revision of the Nuts paper, some conversations about parameterizations of categorical-data models, plans for the R interface, blah blah blah. But also, I had two exciting new ideas! Google Translate for code Wouldn’t it be great if Google Translate could work on computer languages? I suggested this and somebody said that it might be a problem because code isn’t always translatable. But that doesn’t worry so much. Google Translate for human languages isn’t perfect either but it’s a useful guide. If I want to write a message to someone in French or Spanish or Dutch, I wouldn’t just write it in English and run it through Translate. What I do is try my best to write it in the desired language, but I can try out some tricky words or phrases in the translator. Or, if I start by translating, I go back and forth to make sure it all makes sense. An R help-list bot We were talking about how to build a Stan commun
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Introduction: I had an email exchange with Patrick Steigler the other day that amused me, so I’ll share it with you. Steigler started with the subject line “Taleb and STDEV vs. MAD” and the message: I came across http://www.edge.org/response-detail/25401 and was wondering what your thoughts on the issue might be. My reply: How come they never ask me for my opinions in these surveys? Steigler: Maybe you need to write a book of aphorisms. me: There’s this: http://andrewgelman.com/2009/05/24/handy_statistic/ and then this, which some students collected from a course I taught: http://www.stat.columbia.edu/~gelman/book/gelman_quotes.pdf Steigler: So, what would you opinion be on the scientific idea that is ready for retirement? me: I guess it’s a good thing they didn’t ask me! Steigler: How about the retirement of p value < .05 for significance? me: Yeah, but that’s too easy. It’s like if someone asks for a pop music recommendation and you say The Beatles. Steigler: Tru
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