Archive for e-values

full Bayesian significance test

Posted in Books, Statistics with tags , , , , , , , , , , on December 18, 2014 by xi'an

Among the many comments (thanks!) I received when posting our Testing via mixture estimation paper came the suggestion to relate this approach to the notion of full Bayesian significance test (FBST) developed by (Julio, not Hal) Stern and Pereira, from São Paulo, Brazil. I thus had a look at this alternative and read the Bayesian Analysis paper they published in 2008, as well as a paper recently published in Logic Journal of IGPL. (I could not find what the IGPL stands for.) The central notion in these papers is the e-value, which provides the posterior probability that the posterior density is larger than the largest posterior density over the null set. This definition bothers me, first because the null set has a measure equal to zero under an absolutely continuous prior (BA, p.82). Hence the posterior density is defined in an arbitrary manner over the null set and the maximum is itself arbitrary. (An issue that invalidates my 1993 version of the Lindley-Jeffreys paradox!) And second because it considers the posterior probability of an event that does not exist a priori, being conditional on the data. This sounds in fact quite similar to Statistical Inference, Murray Aitkin’s (2009) book using a posterior distribution of the likelihood function. With the same drawback of using the data twice. And the other issues discussed in our commentary of the book. (As a side-much-on-the-side remark, the authors incidentally  forgot me when citing our 1992 Annals of Statistics paper about decision theory on accuracy estimators..!)