BAYESIAN INFERENCE IN INCOMPLETE MULTI-WAY TABLES
Adrian Dobra, Claudia Tebaldi and Mike West
February 2003
We describe and illustrate approaches to Bayesian inference
in multi-way contingency tables for which partial information,
in the form of subsets of marginal totals, is available.
In such problems, interest lies in questions of inference about
the parameters of models underlying the table together with
imputation for the individual cell entries. We discuss questions
of structure related to the implications for inference on cell
counts arising from assumptions about log-linear model forms, and
a class of simple and useful prior distributions on the parameters
of log-linear models. We then discuss ``local move'' and ``global move''
Metropolis-Hastings simulation methods for exploring the posterior
distributions for parameters and cell counts, focusing particularly
on higher-dimensional problems. As a by-product, we note potential
uses of the ``global move'' approach for inference about numbers of
tables consistent with a prescribed
subset of marginal counts. Illustration and comparison of MCMC approaches
is given, and we conclude with discussion of areas for
further developments and current open issues.
Keywords:
Bayesian inference; Disclosure limitation;
Fixed margins problem; Imputation;
Log-linear models; Markov basis; Markov chain Monte Carlo; Missing data.
The manuscript (pdf format) is available