Bayesian test of normality versus a Dirichlet process mixture alternative

Details Bayesian test of normality versus a Dirichlet process mixture alternative Bayesian test of normality versus a Dirichlet process mixture alternative

2011-08-14

arxiv.org/abs/1108.2883v1

Mathematics

Statistics Theory

22 pages, 4 figures, 2 tables

Scientific paper

Testing if a $p$-dimensional sample, for $p \geq 1$, comes from a normal population is a fundamental problem in statistics. In this paper we propose a Bayesian test of $p$-variate normality against an alternative hypothesis characterized by a certain Dirichlet process mixture model. It is shown that this nonparametric alternative satisfies the desirable embedding and predictive matching properties with respect to the normal null model. To compute the Bayes factor, an efficient sequential importance sampler is is proposed for evaluating the marginal likelihood under the nonparametric alternative. Numerical examples show that the proposed test has satisfactory discriminatory power when the distribution is not normal, and does not tend to over-fit when the distribution is normal.

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