Today was day two of ISBA, the big international Bayesian conference. In my session—which was on statistics in astronomy—I spoke about exoplanet search and population inferences (work with Foreman-Mackey, Wang, and Schölkopf), Xiao-Li Meng (Harvard) spoke about instrument calibration, and David van Dyk (ICL) spoke about Bayesian alternatives to p-values for physics and astronomy. Meng had very valuable things to say about taking an inference problem from the linear domain (where calibration multiplies linear flux) to the log domain (where log calibration adds to log flux). I learned a lot that is of relevance to things like self-calibration, where I think maybe we have been going to the log domain (very slightly) incorrectly! There is a half-sigma correction floating around!
van Dyk made the center of his presentation the five-sigma discovery of the Higgs Boson; he pointed out that five-sigma is very conservative in principle, but the fact that it has been applied to as many hypotheses as there are relatively different Higgs mass options makes it less conservative. This isn't trivial to deal with if the only question is whether or not there is a Higgs. He solved the problem in some Bayesian contexts and compared to frequentist multiple-hypothesis solutions. Interestingly, he isn't against using p-values in the discovery context (especially when billions of dollars of public money are at stake); 5-sigma p-values are conservative, and (more importantly) perceived to be conservative!
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