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Random sampling of contingency tables via probabilistic divide-and-conquer

Author

Listed:
  • Stephen DeSalvo

    (UCLA Department of Mathematics)

  • James Zhao

    (USC Department of Mathematics)

Abstract

We present a new approach for random sampling of contingency tables of any size and constraints based on a recently introduced probabilistic divide-and-conquer (PDC) technique. Our first application is a recursive PDC: it samples the least significant bit of each entry in the table, motivated by the fact that the bits of a geometric random variable are independent. The second application is via PDC deterministic second half, where one divides the sample space into two pieces, one of which is deterministic conditional on the other; this approach is highlighted via an exact sampling algorithm in the $$2\times n$$2×n case. Finally, we also present a generalization to the sampling algorithm where each entry of the table has a specified marginal distribution.

Suggested Citation

  • Stephen DeSalvo & James Zhao, 2020. "Random sampling of contingency tables via probabilistic divide-and-conquer," Computational Statistics, Springer, vol. 35(2), pages 837-869, June.
    • Handle: RePEc:spr:compst:v:35:y:2020:i:2:d:10.1007_s00180-019-00899-7
    DOI: 10.1007/s00180-019-00899-7
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    References listed on IDEAS

    as
    1. Yuguo Chen & Persi Diaconis & Susan P. Holmes & Jun S. Liu, 2005. "Sequential Monte Carlo Methods for Statistical Analysis of Tables," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 109-120, March.
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