Recursive pathways to marginal likelihood estimation with prior-sensitivity analysis

Cameron, Ewan & Pettitt, Anthony N. (2014) Recursive pathways to marginal likelihood estimation with prior-sensitivity analysis. Statistical Science, 29(3), pp. 397-419.

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Abstract

We investigate the utility to computational Bayesian analyses of a particular family of recursive marginal likelihood estimators characterized by the (equivalent) algorithms known as "biased sampling" or "reverse logistic regression" in the statistics literature and "the density of states" in physics. Through a pair of numerical examples (including mixture modeling of the well-known galaxy dataset) we highlight the remarkable diversity of sampling schemes amenable to such recursive normalization, as well as the notable efficiency of the resulting pseudo-mixture distributions for gauging prior-sensitivity in the Bayesian model selection context. Our key theoretical contributions are to introduce a novel heuristic ("thermodynamic integration via importance sampling") for qualifying the role of the bridging sequence in this procedure, and to reveal various connections between these recursive estimators and the nested sampling technique.

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6 citations in Scopus
7 citations in Web of Science®
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ID Code: 70707
Item Type: Journal Article
Refereed: Yes
Additional URLs:
Keywords: Bayes factor, Bayesian model selection, importance sampling, marginal likelihood, Metropolis-coupled Markov Chain Monte Carlo, nested sampling, normalizing constant, path sampling, reverse logistic regression, thermodynamic integration
DOI: 10.1214/13-STS465
ISSN: 0883-4237
Divisions: Current > QUT Faculties and Divisions > Science & Engineering Faculty
Funding:
Copyright Owner: Copyright 2014 Institute of Mathematical Statistics
Deposited On: 29 Apr 2014 22:52
Last Modified: 21 Jun 2017 02:01

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