Asymptotic Enumeration of Binary Contingency Tables and Comparison with Independence Heuristic
Da Wu

TL;DR
This paper derives precise asymptotic counts for certain high-dimensional binary contingency tables with non-uniform margins and shows that the classical independence heuristic significantly overestimates their number, especially as dimensions grow.
Contribution
It provides a sharp asymptotic formula for counting binary contingency tables with non-uniform margins and compares it to the independence heuristic, revealing overestimation factors.
Findings
Asymptotic formula for contingency tables with non-uniform margins
Independence heuristic overestimates counts by exponential factor
Explicit bounds for correlation ratio constants
Abstract
For parameters , we obtained a sharp asymptotic formula for the number of -dimensional binary contingency tables with non-uniform margins taking values of and . Furthermore, we compared our sharp asymptotics with the classical independence heuristic estimate and proved that the independence heuristic overestimates by a factor of . Our comparison is based on the analysis of the correlation ratio and an explicit bound for the constant in is also obtained.
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Taxonomy
TopicsMarkov Chains and Monte Carlo Methods · Random Matrices and Applications · Statistical Methods and Inference
