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Conditional inference given partial information in contingency tables using Markov bases

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Abstract In this article, we review a Markov chain Monte Carlo (MCMC) algorithm for performing conditional inference in contingency tables in the presence of partial information using Markov bases, a key tool arising from the area known as algebraic statistics. We review applications of this algorithm to the problems of conditional exact tests, ecological inference, and disclosure limitation and illustrate how these problems fall naturally in the setting of inference with partial information. We also discuss some issues associated with computing Markov bases which are needed as an input to the algorithm. WIREs Comput Stat 2013, 5:207–218. doi: 10.1002/wics.1256 This article is categorized under: Data: Types and Structure > Traditional Statistical Data

MCMC algorithm to sample from P(n,p|𝒯 ,ℳ︁).

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Distribution of cell counts in Voting by Race example. (a) 𝒯 conditional rates; (b) 𝒯 = conditional rates and marginal counts.

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