2019/02/28 by David J. Nott, Max Seah, Luai Al-Labadi +3
Computer Science · Mathematics · Physics and Astronomy · #Bayesian probability #Exponential family #Gaussian Processes and Bayesian Inference #Markov Chains and Monte Carlo Methods #Model checking #Multinomial distribution #Prior probability #Statistic #Statistical Methods and Inference #quant-ph #stat.ME
paper · pdf · doi:10.1214/20-ba1204
Accepted version, to appear in Bayesian Analysis
openalex created_date 2019/03/02 · arxiv created 2020/03/12 · openalex publication_date 2020/03/28 · arxiv updated 2020/08/04 · openalex updated_date 2026/08/05
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.