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Investigation of the widely applicable Bayesian information criterion
Date Issued
2017-05
Date Available
2017-05-19T01:00:12Z
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.
Sponsorship
Science Foundation Ireland
Other Sponsorship
Australian Postgraduate Award (APA)
Australian Research Council Discovery Grant
Type of Material
Journal Article
Publisher
Springer
Journal
Statistics and Computing
Volume
27
Issue
3
Start Page
833
End Page
844
Copyright (Published Version)
2016 Springer
Language
English
Status of Item
Peer reviewed
This item is made available under a Creative Commons License
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Name
Investigation of the widely applicable bayesian information criterion.pdf
Size
556.43 KB
Format
Owning collection
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