Fernando Llorente and (Madrilene) coauthors have just arXived a paper on the safe use of prior densities for Bayesian model selection. Rather than blaming the Bayes factor, or excommunicating some improper priors, they consider in this survey solutions to design “objective” priors in model selection. (Writing this post made me realised I had forgotten to […]

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## prior sensitivity of the marginal likelihood

June 27, 2022## [more than] everything you always wanted to know about marginal likelihood

February 10, 2022Earlier 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 […]

## marginal likelihood with large amounts of missing data

October 20, 2020In 2018, Panayiota Touloupou, research fellow at Warwick, and her co-authors published a paper in Bayesian analysis that somehow escaped my radar, despite standing in my first circle of topics of interest! They construct an importance sampling approach to the approximation of the marginal likelihood, the importance function being approximated from a preliminary MCMC run, […]

## marginal likelihood as exhaustive X validation

October 9, 2020In the June issue of Biometrika (for which I am deputy editor) Edwin Fong and Chris Holmes have a short paper (that I did not process!) on the validation of the marginal likelihood as the unique coherent updating rule. Marginal in the general sense of Bissiri et al. (2016). Coherent in the sense of being […]

## estimating the marginal likelihood (or an information criterion)

December 28, 2019Tory Imai (from Kyoto University) arXived a paper last summer on what first looked like a novel approximation of the marginal likelihood. Based on the variance of thermodynamic integration. The starting argument is that there exists a power 0<t⁰<1 such that the expectation of the logarithm of the product of the prior by the likelihood […]