I spent my research time today working through the final draft of Hou's paper on computing the fully marginalized likelihood (the FML, the Bayes integral, or the evidence integral) using a geometric-path Monte Carlo method we invented-ish with Goodman. The idea is simple: The BIC is an approximation to the FML that replaces the likelihood with a Gaussian approximation. You can build an intermediate approximation to the FML that replaces the likelihood with the geometric mean of a Gaussian and the true likelihood. As you can imagine, there is a whole family of such approximations, going from the pure Gaussian approximation to the true likelihood. We travel along this "geometric path" from the Gaussian to the true likelihood and end up with an estimate of the FML. The method is fast and effective in exoplanet contexts (as we show) but is also unbiased and also produces an uncertainty estimate on the FML computation it produces.
Sounds rather like Lefebvre et al. 2010. My posterior probability that a method is new after being told it's new is typically <0.05 :-)
ReplyDeleteYes, didn't mean to claim novelty! Just invention.
Deleteps. Can you post a reference; we can't find the paper.
DeleteA path sampling identity for computing the Kullback–Leibler and J divergences, Lefebvre et al in CSDA is the one I was thinking of. http://tiny.cc/jdivergence
DeleteThese guys also have a (somewhat convoluted) investigation of geometric path-based estimators:
ReplyDeletehttp://xxx.tau.ac.il/pdf/1308.6753.pdf