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Relevant statistics for Bayesian model choice
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Marin, Jean-Michel, Pillai, Natesh S., Robert, Christian P. and Rousseau, Judith (2014) Relevant statistics for Bayesian model choice. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 76 (5). pp. 833-859. doi:10.1111/rssb.12056
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Official URL: http://dx.doi.org/10.1111/rssb.12056
Abstract
The choice of the summary statistics that are used in Bayesian inference and in particular in approximate Bayesian computation algorithms has bearings on the validation of the resulting inference. Those statistics are nonetheless customarily used in approximate Bayesian computation algorithms without consistency checks. We derive necessary and sufficient conditions on summary statistics for the corresponding Bayes factor to be convergent, namely to select the true model asymptotically. Those conditions, which amount to the expectations of the summary statistics differing asymptotically under the two models, are quite natural and can be exploited in approximate Bayesian computation settings to infer whether or not a choice of summary statistics is appropriate, via a Monte Carlo validation.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Divisions: | Faculty of Science > Statistics | ||||
| Journal or Publication Title: | Journal of the Royal Statistical Society: Series B (Statistical Methodology) | ||||
| Publisher: | Wiley-Blackwell Publishing Ltd. | ||||
| ISSN: | 1369-7412 | ||||
| Official Date: | 2014 | ||||
| Dates: |
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| Volume: | 76 | ||||
| Number: | 5 | ||||
| Page Range: | pp. 833-859 | ||||
| DOI: | 10.1111/rssb.12056 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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