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Pseudo-Gibbs sampler for discrete conditional distributions

Author

Listed:
  • Kun-Lin Kuo

    (National University of Kaohsiung)

  • Yuchung J. Wang

    (Rutgers University)

Abstract

Conditionally specified models offers a higher level of flexibility than the joint approach. Regression switching in multiple imputation is a typical example. However, reasonable-seeming conditional models are generally not coherent with one another. Gibbs sampler based on incompatible conditionals is called pseudo-Gibbs sampler, whose properties are mostly unknown. This article investigates the richness and commonalities among their stationary distributions. We show that Gibbs sampler replaces the conditional distributions iteratively, but keep the marginal distributions invariant. In the process, it minimizes the Kullback–Leibler divergence. Next, we prove that systematic pseudo-Gibbs projections converge for every scan order, and the stationary distributions share marginal distributions in a circularly fashion. Therefore, regardless of compatibility, univariate consistency is guaranteed when the orders of imputation are circularly related. Moreover, a conditional model and its pseudo-Gibbs distributions have equal number of parameters. Study of pseudo-Gibbs sampler provides a fresh perspective for understanding the original Gibbs sampler.

Suggested Citation

  • Kun-Lin Kuo & Yuchung J. Wang, 2019. "Pseudo-Gibbs sampler for discrete conditional distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(1), pages 93-105, February.
    • Handle: RePEc:spr:aistmt:v:71:y:2019:i:1:d:10.1007_s10463-017-0625-x
    DOI: 10.1007/s10463-017-0625-x
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    References listed on IDEAS

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    1. Kuo, Kun-Lin & Wang, Yuchung J., 2011. "A simple algorithm for checking compatibility among discrete conditional distributions," Computational Statistics & Data Analysis, Elsevier, vol. 55(8), pages 2457-2462, August.
    2. Chen, Shyh-Huei & Ip, Edward H. & Wang, Yuchung J., 2011. "Gibbs ensembles for nearly compatible and incompatible conditional models," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1760-1769, April.
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    Cited by:

    1. Kun-Lin Kuo & Yuchung J. Wang, 2023. "Analytical Computation of Pseudo-Gibbs Distributions for Dependency Networks," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-17, March.

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