MCMC Sampling Estimation of Poisson-Dirichlet Process Mixture Models

In this article, we aim to estimate the parameters of Poisson-Dirichlet mixture model with multigroup data structure by empirical Bayes. The number of mixture components with Bayesian nonparametric process priors is not fixed in advance and it can grow with the increase of data. Empirical Bayes is the useful method to estimate the mixture components without information on them in advance. We give the procedure to construct smooth estimates of base distribution <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <msub> <mrow> <mi>G</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </math> and estimates of the two parameters <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"> <mfenced open="(" close=")" separators="|"> <mrow> <mi>α</mi> <mo>,</mo> <mi>θ</mi> </mrow> </mfenced> </math> . The performances of estimations for parameters under multigroup data are better than those of the single-group data with the same total size of individuals in the perspectives of bias, standard deviations, and mean squared errors by numerical simulation. Also, we applied Poisson-Dirichlet mixture models to well-known real datasets.