Goodness-of-Fit Tests for High-dimensional Discrete Distributions with Application to Convergence Diagnostics in Approximate Bayesian Inference. Saad, F. A., Freer, C. E., Ackerman, N. L., & Mansinghka, V. K. In AABI 2018: 1st Symposium on Advances in Approximate Bayesian Inference, 2018.
Goodness-of-Fit Tests for High-dimensional Discrete Distributions with Application to Convergence Diagnostics in Approximate Bayesian Inference [pdf]Paper  abstract   bibtex   
We present a new family of goodness-of-fit tests that is specialized to high-dimensional discrete distributions. The proposed test is readily implemented using a simple simulationbased procedure and can be computed in linear time, and it can be customized by the practitioner using knowledge of the underlying data domain. Unlike most existing statistics, the proposed test statistic is distribution-free and has an exact (non-asymptotic) sampling distribution. We establish consistency of the test by showing the statistic is distributed as a discrete uniform if and only if the samples are drawn from the candidate distribution. We use the test to assess the convergence behavior of sampling algorithms for approximate Bayesian inference of random partitions in Dirichlet process mixture models.

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