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2138 andrew gelman stats-2013-12-18-In Memoriam Dennis Lindley


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Introduction: So. Farewell then Dennis Lindley. You held the Hard line on Bayesianism When others Had doubts. And you share The name of a famous Paradox. What is your subjective Prior now? We can only Infer. R. A. Thribb (17 1/2) P.S.


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1 You held the Hard line on Bayesianism When others Had doubts. [sent-3, score-0.741]


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Introduction: So. Farewell then Dennis Lindley. You held the Hard line on Bayesianism When others Had doubts. And you share The name of a famous Paradox. What is your subjective Prior now? We can only Infer. R. A. Thribb (17 1/2) P.S.

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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: A couple days ago we discussed some remarks by Tony O’Hagan and Jim Berger on weakly informative priors. Jim followed up on Deborah Mayo’s blog with this: Objective Bayesian priors are often improper (i.e., have infinite total mass), but this is not a problem when they are developed correctly. But not every improper prior is satisfactory. For instance, the constant prior is known to be unsatisfactory in many situations. The ‘solution’ pseudo-Bayesians often use is to choose a constant prior over a large but bounded set (a ‘weakly informative’ prior), saying it is now proper and so all is well. This is not true; if the constant prior on the whole parameter space is bad, so will be the constant prior over the bounded set. The problem is, in part, that some people confuse proper priors with subjective priors and, having learned that true subjective priors are fine, incorrectly presume that weakly informative proper priors are fine. I have a few reactions to this: 1. I agree

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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: 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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