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

Author

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  • Liu Yang

    (Worcester Polytechnic Institute, USA .)

  • Nandram Balgobin

    (Worcester Polytechnic Institute, USA .)

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 hyper-parameters: 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.

Suggested Citation

  • Liu Yang & Nandram Balgobin, 2022. "Sampling methods for the concentration parameter and discrete baseline of the Dirichlet Process," Statistics in Transition New Series, Statistics Poland, vol. 23(4), pages 21-36, December.
  • Handle: RePEc:vrs:stintr:v:23:y:2022:i:4:p:21-36:n:10
    DOI: 10.2478/stattrans-2022-0040
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    References listed on IDEAS

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    1. Sanjay Chaudhuri & Malay Ghosh, 2011. "Empirical likelihood for small area estimation," Biometrika, Biometrika Trust, vol. 98(2), pages 473-480.
    2. Teh, Yee Whye & Jordan, Michael I. & Beal, Matthew J. & Blei, David M., 2006. "Hierarchical Dirichlet Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1566-1581, December.
    3. Ishwaran H. & James L. F, 2001. "Gibbs Sampling Methods for Stick Breaking Priors," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 161-173, March.
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