Sampling methods for the concentration parameter and discrete baseline of the Dirichlet Process

Yang Liu; Balgobin Nandram

doi:10.2478/stattrans-2022-0040

Sampling methods for the concentration parameter and discrete baseline of the Dirichlet Process

Yang Liu Worcester Polytechnic Institute, USA ORCID:https://orcid.org/0000-0003-1414- 0349 , Balgobin Nandram Worcester Polytechnic Institute, USA ORCID:https://orcid.org/0000-0002-3204- 0301 Statistics in Transition new series, vol. 23, 2022, 4, pages: 21-36 Published online: 15 December 2022 DOI 10.2478/stattrans-2022-0040

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ARTICLE

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ABSTRACT

There are many models in the 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) prior is very flexible and determines the complexity of the model. It is indexed by two hyperparameters: the baseline distribution and concentration parameter. We address two distinct problems in the article. Firstly, we review the current sampling methods for the concentration parameter, which use the continuous baseline distribution. We compare three different methods: the adaptive rejection method, the mixture of Gammas method and the grid method. We also propose a new method based on the ratio of uniforms. Secondly, 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 inference may be invalid. We propose a discrete baseline approach to the DP prior and sample the unobserved responses from the finite population both using a Polya urn scheme and a Multinomial distribution. We applied our discrete baseline approach to a Phytophthora data set.

KEYWORDS

concentration parameter, discrete baseline, empirical study, grid method, nonparametric Bayesian statistics

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