On the number of contingency tables and the independence heuristic

09/22/2020

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by   Hanbaek Lyu, et al.

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We obtain sharp asymptotic estimates on the number of n × n contingency tables with two linear margins Cn and BCn. The results imply a second order phase transition on the number of such contingency tables, with a critical value at B_c:=1 + √(1+1/C). As a consequence, for B>B_c, we prove that the classical independence heuristic leads to a large undercounting.