Bayesian Measures of Goodness of Fit

Abstract

While determining the goodness of fit of a model is not a necessary step in a traditional Bayesian analysis, in practice, one should verify if the model proposed is indeed a good fit to the data. A review of methods for critical assessment of the appropriateness of fitted Bayesian models is considered in this work. This is done for situations where no particular alternative model is specified and where the discrepancy between model and data is measurable in a user‐defined way. Methods for testing goodness of fit in nonhierarchical models are discussed before discussing hierarchical models. These methods are done in light of MCMC sampling with its abilities and challenges.