We describe and illustrate approaches to Bayesian inference in partially observed contingency tables. Key examples include problems of observation of only selected marginal totals, when interest lies in inference about unobserved cell counts and underlying cell probabilities. A main focus of this work is the presentation and illustration of a novel and efficient simulation algorithm for imputation of missing cell counts and its incorporation into Bayesian analyses of partially observed tables. We present and illustrate the algorithm in a context of two-way tables, where we also introduce a new and flexible class of prior distributions for parameters in saturated log-linear models. Illustration is provided using data arising from a NISS transportation policy research project, and a second data set used to compare the approach with existing and standard algorithms. This second example illustrates the practical efficacy of the new imputation, and the major extent to which it dominates existing methods from an applied point of view.

Keywords: Bayesian inference; Imputation; Missing data; Log-linear models; Markov chain Monte Carlo.

The research reported here was partially supported by NSF grant DMS-9313013 to the National Institute of Statistical Sciences.

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