tag:blogger.com,1999:blog-10448119.post760788886937348477..comments2024-03-29T07:56:43.514-04:00Comments on Hogg's Research: marginalized likelihood, goose eggHogghttp://www.blogger.com/profile/18398397408280534592noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-10448119.post-59153635911672826162013-09-27T01:31:42.816-04:002013-09-27T01:31:42.816-04:00I reckon people tend to over-complicate the margin...I reckon people tend to over-complicate the marginal likelihood calculation: if you are already exploring the posterior via parallel-tempered MCMC then the biased sampling method (Vardi 1985; / my recursive pathway paper) gives you immediately a good estimate with a CLT uncertainty estimate. <br />For some reason this information is often thrown away by astronomers in favour of the harmonic or arithmetic mean type estimators. E.g. the BIE [Weinberg et al.] does tempered transitions but doesn't use them for marginal likelihood estimator; likewise the ctsmod code for stochastic time-series modelling by Bailer-Jones.<br /><br />The other nice thing about biased sampling (also called reverse logistic regresion, or the density of states) is that it allows easy prior-sensitivity analysis via importance sample reweighting (using the Radon-Nikodym derivative for stochastic process models; which has a well-defined limiting form for the Gaussian process). Anonymousnoreply@blogger.com