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dominating measure

March 21, 2019

Yet another question on X validated reminded me of a discussion I had once  with Jay Kadane when visiting Carnegie Mellon in Pittsburgh. Namely the fundamentally ill-posed nature of conjugate priors. Indeed, when considering the definition of a conjugate family as being a parameterised family Þ of distributions over the parameter space Θ stable under […]

estimating the measure and hence the constant

December 6, 2012

As mentioned on my post about the final day of the ICERM workshop, Xiao-Li Meng addresses this issue of “estimating the constant” in his talk. It is even his central theme. Here are his (2011) slides as he sent them to me (with permission to post them!): He therefore points out in slide #5 why […]

essentials of probability theory for statisticians

April 25, 2020

On yet another confined sunny lazy Sunday morning, I read through Proschan and Shaw’s Essentials of Probability Theory for Statisticians, a CRC Press book that was sent to me quite a while ago for review. The book was indeed published in 2016. Before moving to serious things, let me evacuate the customary issue with the […]

posterior distribution missing the MLE

April 25, 2019

An X validated question as to why the MLE is not necessarily (well) covered by a posterior distribution. Even for a flat prior… Which in restrospect highlights the fact that the MLE (and the MAP) are invasive species in a Bayesian ecosystem. Since they do not account for the dominating measure. And hence do not […]

p-values, Bayes factors, and sufficiency

April 15, 2019

Among the many papers published in this special issue of TAS on statistical significance or lack thereof, there is a paper I had already read before (besides ours!), namely the paper by Jonty Rougier (U of Bristol, hence the picture) on connecting p-values, likelihood ratio, and Bayes factors. Jonty starts from the notion that the […]