Random Sampling of Contingency Tables via Probabilistic Divide-and-Conquer

TL;DR

This paper introduces a novel probabilistic divide-and-conquer method for efficiently and exactly sampling contingency tables of any size, including those with specified marginal distributions, advancing statistical sampling techniques.

Contribution

It presents a new exact sampling algorithm for 2×n tables and generalizes it to tables with entries having specified marginal distributions.

Findings

Efficient exact sampling for 2×n contingency tables.

Generalization to tables with specified marginal distributions.

Introduction of a probabilistic divide-and-conquer approach.

Abstract

We present a new approach for random sampling of contingency tables of any size and constraints based on a recently introduced $\textit{probabilistic divide-and-conquer}$ technique. A simple exact sampling algorithm is presented for $2\times n$ tables, as well as a generalization where each entry of the table has a specified marginal distribution.