Investigation of the widely applicable Bayesian information criterion

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Title: Investigation of the widely applicable Bayesian information criterion
Authors: Friel, Nial
McKeone, J. P.
Oates, Chris J.
Pettitt, Anthony
Permanent link: http://hdl.handle.net/10197/8392
Date: May-2017
Abstract: The widely applicable Bayesian information criterion (WBIC) is a simple and fast approximation to the model evidence that has received little practical consideration. WBIC uses the fact that the log evidence can be written as an expectation, with respect to a powered posterior proportional to the likelihood raised to a power t(0,1)t(0,1) , of the log deviance. Finding this temperature value tt is generally an intractable problem. We find that for a particular tractable statistical model that the mean squared error of an optimally-tuned version of WBIC with correct temperature tt is lower than an optimally-tuned version of thermodynamic integration (power posteriors). However in practice WBIC uses the a canonical choice of t=1/log(n)t=1/log(n) . Here we investigate the performance of WBIC in practice, for a range of statistical models, both regular models and singular models such as latent variable models or those with a hierarchical structure for which BIC cannot provide an adequate solution. Our findings are that, generally WBIC performs adequately when one uses informative priors, but it can systematically overestimate the evidence, particularly for small sample sizes.
Funding Details: Science Foundation Ireland
Type of material: Journal Article
Publisher: Springer
Copyright (published version): 2016 Springer
Keywords: Machine learning;Statistics;Marginal likelihood;Evidence;Power posteriors;Widely applicable Bayesian information criterion
DOI: 10.1007/s11222-016-9657-y
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection
Insight Research Collection

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