JSM 2011 [2]

Yesterday at JSM 2011 was a slow start as I only attended the last session of the Sunday afternoon. (After completing recycling my class slides for the roundtable on Tuesday, exploring the Art Déco neighbourhood of the convention center, fighting the clamy heat by periodically dropping into AC stores, including the Apple store on Lincoln Mall, buying a much needed umbrella for my beach-deprived kids and finding a glasses store that kindly replaced a lost tiny screw on my daughter’s sunglasses, …) This was session 67, Bayesian methods in lifetime and longitudinal data. As is presumably the case for most late Sunday afternoon sessions in a massively parallel universe (89-44=45 sessions!), the room was filled by the speakers, the chairwoman and very few listeners…

The talks that had driven me to the far end of the convention centre, half a mile away from the registration desk!, were Sanjib Basu’s on Bayesian model comparison and Sanjay Chaudhuri’s on Bayesian empirical likelihood. Empirical likelihood remains for me a difficult concept in that it somehow clashes with the Bayesian paradigm: if there is no model and no likelihood, it seems delicate (a) to apply Bayes’ theorem and (b) to construct a prior distribution. I only have vague thoughts about the issue, but there should be a more Bayesian way of constructing the estimate of the likelihood function under the constraints, rather than using maximisation. (I think this is alluded to and somehow dismissed in Lazar’s 2005 Biometrika paper.) While mentioning some theoretical justifications for the approach, Sanjay’s talk also covered the more methodological issue of zero values in the empirical likelihood leading to a non-connected support. I do not know whether or not the classical theory brings a solution to this problem (again, having no connection at my rental does not help!), but I wonder if reparameterisation could help in this respect. The talk by Sanjib was about very familiar ground (see e.g. our San Antonio chapter), namely approximation methods for computing Bayes factors. He also ran a small experiment to compare Bayes factors with predictive pseudo-likelihood (i.e., Bayesian cross-validation) approximations and with DIC (discussed in the Bayesian Choice). I was a bit takecn aback when Sanjib suggested a return to the dreaded harmonic mean estimator as he had no guarantee his estimator was free from an infinite variance. When discussing with him later, I pointed out our alternative harmonic mean representation using HPD regions and he mentioned a 1997 paper by Tom DiCiccio doing something similar that I need to check.

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