Counting subsets of contingency tables

George Fishman ()

Computational Statistics, 2014, vol. 29, issue 1, 159-187

Abstract: We describe multistage Markov chain Monte Carlo (MSMCMC) procedures which, in addition to estimating the total number of contingency tables with given positive row and column sums, estimate the number, $$Q$$ Q , and the proportion, $$P$$ P , of those tables that satisfy an additional, possibly, nonlinear constraint. Three Options, A, B, and C, are studied. Options A and B exploit locally optimal statistical properties whereas judicious assignment of a particular parameter of Option C allows estimation with approximately minimal standard error. Ten examples of varying dimensions and total entries illustrate and compare the procedures, where $$Q$$ Q and $$P$$ P denote the number and proportion of chi-squared statistics less than a given value. For both small and large dimensional tables, the comparisons favor Options A and B for moderate $$P$$ P and Option C for small $$P$$ P . Additional comparison with sequential importance sampling estimates favors the latter for small dimensional tables and moderate $$P$$ P but favors Option C for large dimensional tables for both small and moderate $$P$$ P . The proposed options extend an earlier MSMCMC technique for estimating total count and, in principle, can be further extended to incorporate additional constraints. Copyright Springer-Verlag Berlin Heidelberg 2014

Keywords: Hastings–Metropolis sampling; Markov chain Monte Carlo; Sequential importance sampling (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:compst:v:29:y:2014:i:1:p:159-187

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DOI: 10.1007/s00180-013-0442-5

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