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Bayesian Test of Normality Versus a Dirichlet Process Mixture Alternative

Surya T. Tokdar () and Ryan Martin
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Surya T. Tokdar: Duke University
Ryan Martin: North Carolina State University

Sankhya B: The Indian Journal of Statistics, 2021, vol. 83, issue 1, No 4, 66-96

Abstract: Abstract We propose a Bayesian test of normality for univariate or multivariate data against alternative nonparametric models characterized by Dirichlet process mixture distributions. The alternative models are based on the principles of embedding and predictive matching. They can be interpreted to offer random granulation of a normal distribution into a mixture of normals with mixture components occupying a smaller volume the farther they are from the distribution center. A scalar parametrization based on latent clustering is used to cover an entire spectrum of separation between the normal distributions and the alternative models. An efficient sequential importance sampler is developed to calculate Bayes factors. Simulations indicate the proposed test can detect non-normality without favoring the nonparametric alternative when normality holds.

Keywords: Bayes factor; embedding; goodness-of-fit; importance sampling; noninformative prior; predictive matching; Primary 62H15; Secondary 62G07 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13571-019-00210-0

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Handle: RePEc:spr:sankhb:v:83:y:2021:i:1:d:10.1007_s13571-019-00210-0