A Bayesian Method for Evaluating Fit of Discrete Distributions

Kert Viele

Abstract:

We develop and extend a Bayesian method for evaluating fit based on model embeddings proposed by Carota, Parmigiani, and Polson (1996). We demonstrate the prior distribution chosen over the large class of models has a potentially strong effect on the inferences and suggest how to create a prior distribution more consistent with the idea of evaluating fit. We illustrate the method for evaluating the fit of a single discrete distribution and show how the method may be extended to evaluating components of a hierarchical model. We compare the method to predictive methods for evaluating fit, showing that the interpretation of predictive results depends strongly on the sample size. We also show a rate of convergence result for Dirichlet Processes.

Keywords: Poisson Distribution, Goodness of Fit, Kullback-Leibler Divergence, Hierarchical Models, Posterior Predictive p-value.

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