Any Bayesian analysis involves combining information represented through different model components, and when different sources of information are in conflict it is important to detect this. Here we consider checking for prior-data conflict in Bayesian models by expanding the prior used for the analysis into a larger family of priors, and considering a marginal likelihood score statistic for the expansion parameter. Consideration of different expansions can be informative about the nature of any conflict, and an appropriate choice of expansion can provide more sensitive checks for conflicts of certain types. Extensions to hierarchically specified priors and connections with other approaches to prior-data conflict checking are considered, and implementation in complex situations is illustrated with two applications. The first concerns testing for the appropriateness of a LASSO penalty in shrinkage estimation of coefficients in linear regression. Our method is compared with a recent suggestion in the literature designed to be powerful against alternatives in the exponential power family, and we use this family as the prior expansion for constructing our check. A second application concerns a problem in quantum state estimation, where a multinomial model is considered with physical constraints on the model parameters. In this example, the usefulness of different prior expansions is demonstrated for obtaining checks which are sensitive to different aspects of the prior.
This work is funded by the Singapore Ministry of Education and the National Research Foundation of Singapore. David Nott was supported by a Singapore Ministry of Education Academic Research Fund Tier 1 grant (R-155-000-189-114). Hui Khoon Ng is funded by a Yale-NUS College start-up grant. Michael Evans was supported by a grant from the Natural Sciences and Engineering Research Council of Canada.
"Using Prior Expansions for Prior-Data Conflict Checking." Bayesian Anal. 16 (1) 203 - 231, March 2021. https://doi.org/10.1214/20-BA1204