Evaluating Fit Using Dirichlet Processes

Kert Viele

Abstract:

We describe a method for quantifying the lack of fit in a proposed family of distributions. The method involves estimating the posterior distribution of the Kullback-Leibler information between the true distribution generating the data and the proposed family. We show Dirichlet Process priors provide a consistent estimate of the KL information and illustrate the method with several real and simulated examples.

Keywords: Goodness of Fit, Kullback-Leibler Information, Consistency

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