the [not so infamous] arithmetic mean estimator

“Unfortunately, no perfect solution exists.” Anna Pajor Another paper about harmonic and not-so-harmonic mean estimators that I (also) missed came out last year in Bayesian Analysis. The author is Anna Pajor, whose earlier note with Osiewalski I also spotted on the same day. The idea behind the approach [which belongs to the branch of Monte […]

On Congdon’s estimator

I got the following email from Bob: I’ve been looking at some methods for Bayesian model selection, and read your critique in Bayesian Analysis of Peter Congdon’s method. I was wondering if it could be fixed simply by including the prior densities of the pseudo-priors in the calculation of P(M=k|y), i.e. simply removing the approximation […]

Split Sampling: expectations, normalisation and rare events

Just before Christmas (a year ago), John Birge, Changgee Chang, and Nick Polson arXived a paper with the above title. Split sampling is presented a a tool conceived to handle rare event probabilities, written in this paper as where π is the prior and L the likelihood, m being a large enough bound to make […]

Another harmonic mean

Yet another paper that addresses the approximation of the marginal likelihood by a truncated harmonic mean, a popular theme of mine. A 2020 paper by Johannes Reich, entitled Estimating marginal likelihoods from the posterior draws through a geometric identity and published in Monte Carlo Methods and Applications. The geometric identity it aims at exploiting is […]

[more than] everything you always wanted to know about marginal likelihood

Earlier this year, F. Llorente, L. Martino, D. Delgado, and J. Lopez-Santiago have arXived an updated version of their massive survey on marginal likelihood computation. Which I can only warmly recommend to anyone interested in the matter! Or looking for a base camp to initiate a graduate project. They break the methods into four families […]