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

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...

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Bibliographic Details
Published in:Computational statistics Vol. 35; no. 2; pp. 837 - 869
Main Authors: DeSalvo, Stephen, Zhao, James
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2020
Springer Nature B.V
Subjects:
Algorithms
Contingency
Contingency tables
Economic Theory/Quantitative Economics/Mathematical Methods
Mathematics and Statistics
Monte Carlo simulation
Original Paper
Probability and Statistics in Computer Science
Probability theory
Probability Theory and Stochastic Processes
Random sampling
Random variables
Sampling techniques
Statistics
Exact sampling
Boltzmann sampler
Transportation polytope
Approximate sampling
ISSN:0943-4062, 1613-9658
Online Access:Get full text
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Summary: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 × n case. Finally, we also present a generalization to the sampling algorithm where each entry of the table has a specified marginal distribution.
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ISSN:0943-4062
1613-9658
DOI:10.1007/s00180-019-00899-7