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Any Bayesian analysis involves combining information represented throughdifferent model components, and when different sources of information are inconflict it is important to detect this. Here we consider checking forprior-data conflict in Bayesian models by expanding the prior used for theanalysis into a larger family of priors, and considering a marginal likelihoodscore statistic for the expansion parameter. Consideration of differentexpansions can be informative about the nature of any conflict, and extensionsto hierarchically specified priors and connections with other approaches toprior-data conflict checking are discussed. Implementation in complexsituations is illustrated with two applications. The first concerns testing forthe appropriateness of a LASSO penalty in shrinkage estimation of coefficientsin linear regression. Our method is compared with a recent suggestion in theliterature designed to be powerful against alternatives in the exponentialpower family, and we use this family as the prior expansion for constructingour check. A second application concerns a problem in quantum state estimation,where a multinomial model is considered with physical constraints on the modelparameters. In this example, the usefulness of different prior expansions isdemonstrated for obtaining checks which are sensitive to different aspects ofthe prior.

Using prior expansions for prior-data conflict checking