Here are the slides for the Savage-Dickey paradox paper that I gave in San Antonio this morning:
(Any suspected coincidence of the first part with earlier talks is for real!) I have tried to spell out as clearly as possible in the second part the issues of version choices that are at the core of the “paradox”.
Just a reminder that I will teach a very short course on March 17 in San Antonio, Texas, based on our “Introducing Monte Carlo Methods with R” book, in the first day of the meeting Frontiers of Statistical Decision Making and Bayesian Analysis, in honour of Jim Berger, There still are a few places left on the four courses provided that day, register now!
Following Andrew Gelman by a few days, we have now finished with Jean-Michel Marin a survey on importance sampling methods for Bayes factor approximations which is our contribution to a book of essays, Frontiers of Statistical Decision Making and Bayesian Analysis, in honour of Jim Berger, published in conjunction with a conference with the same name, next March, in San Antonio, Texas. When I was young, so much younger than today, I could not see the point of those celebration conferences. I am not sure I have gotten any wiser with age, but I do see a point in celebrating Jim Berger! First, Jim has contributed and is contributing immensely to statistical science from many respects, first and foremost in grounding Bayesian analysis within decision theory. His book Statistical Decision Theory and Bayesian Analysis has influenced many readers and this is certainly the (statistics) book that has had the most influence upon me, as can be seen in The Bayesian Choice
The survey with Jean-Michel, now posted on arXiv, is linked with some older work of Jim in that he was studying importance sampling methods with Man-Suk Oh at the time I was visiting Purdue, in the pre-MCMC days. The toolkit for approximating Bayes factors has considerably grown in the past twenty years but importance sampling, albeit in a refined format, remains a central methodology. In the probit example we provide in the survey, this is actually the best method, thanks to a very good approximation of the posterior by the normal asymptotic approximation to the likelihood, as already shown in the entry on Savage-Dickey posted a few days ago. In this same example, the harmonic mean estimator of the marginal is doing surprisingly well, again because of the fit of the approximation.
After modifying my slides for the Yes III workshop by (a) including a Monte Carlo comparison between importance sampling methods (done in a survey paper with Jean-Michel Marin in preparation for the conference in honour of Jim Berger) and (b) covering the Savage-Dickey latest develoments (another paper soon to be posted), I put those slides on slideshare:
(Warning: the changes only are in the importance sampling section)
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