Bayesian Inference in Incomplete Multi-Way Tables

摘要: Summary We describe and illustrate approaches to Bayesian inference in multi-way contingency ta-bles for which partial information, the form of subsets marginal totals, is available.In such problems, interest lies questions about parameters modelsunderlying table together with imputation individual cell entries. discussquestions structure related implications on counts arising fromassumptions log-linear model forms, a class simple useful prior distribu-tions models. then discuss \local move" \globalmove" Metropolis-Hastings simulation methods exploring posterior distributions forparameters counts, focusing particularly higher-dimensional problems. As by-product, we note potential uses \global approach numbersof tables consistent prescribed subset counts. Illustration compar-ison MCMC given, conclude discussion areas furtherdevelopments current open issues.Some key words: inference; Disclosure limitation; Fixed margins problem; Imputation; Log-linear models; Markov basis; chain Monte Carlo; Missing data.2