Journal
STATISTICAL SCIENCE
Volume 35, Issue 2, Pages 234-253Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/19-STS731
Keywords
Bayesian inference; model checking; prior data-conflict; variational Bayes; Bayesian inference
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Funding
- Singapore Ministry of Education Academic Research Fund Tier 2 grant [R-155000-143-112]
- Singapore Ministry of Education [MOE2012-T3-1009]
- National Research Foundation of Singapore
- Natural Sciences and Engineering Research Council of Canada [10671]
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y When using complex Bayesian models to combine information, checking consistency of the information contributed by different components of the model for inference is good statistical practice. Here a new method is developed for detecting prior-data conflicts in Bayesian models based on comparing the observed value of a prior-to-posterior divergence to its distribution under the prior predictive distribution for the data. The divergence measure used in our model check is a measure of how much beliefs have changed from prior to posterior, and can be thought of as a measure of the overall size of a relative belief function. It is shown that the proposed method is intuitive, has desirable properties, can be extended to hierarchical settings, and is related asymptotically to Jeffreys' and reference prior distributions. In the case where calculations are difficult, the use of variational approximations as a way of relieving the computational burden is suggested. The methods are compared in a number of examples with an alternative but closely related approach in the literature based on the prior predictive distribution of a minimal sufficient statistic.
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