Statistics and Data Science Seminar
Ryan Martin
UIC
A Bayesian test of normality versus a Dirichlet process mixture alternative
Abstract: Testing if a p-dimensional sample, for p >= 1, comes from a normal population is a
fundamental problem in statistics. In this talk I will describe a new Bayesian test of p-variate
normality against an alternative hypothesis characterized by a certain Dirichlet process mixture
model. I will show 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 demonstrate 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.
Wednesday September 7, 2011 at 4:00 PM in SEO 636