347 – Nonparametric Hybrid Methods
Sampling Methods for the Concentration Parameter of the Dirichlet Process
Yang (Lyric) Liu
Worcester Polytechnic Institute
There are many methods in current statistical literature for making inferences based on samples selected from a finite population. Parametric models may be problematic because statistical inference is sensitive to parametric assumptions. The Dirichlet process (DP) is very flexible and determines the complexity of the model. It is indexed by two hyper-parameters: the baseline distribution and concentration parameter. Current sampling methods for the concentration parameter only consider the continuous baseline distribution. We compare three different methods: Adaptive Reject Algorithm, Mixture of Gammas Method and Grid Method. We also propose a new method based on the ratio of uniforms. In practice, some survey responses are known to be discrete; if a continuous distribution is adopted as the baseline distribution, the model is misspecified and standard estimation/inference may be invalid. We propose a discrete baseline approach to the DP and conclude that the unobserved responses from the finite population can be sampled from a multinomial distribution if all possible outcomes are observed. We also applied our discrete baseline approach to a Phytophthora data set.