Bayesian models for sparse probability tables
Jim Q. Smith, Catriona M. Queen
The Annals of Statistics · 1996 · Volume 24 · Issue 5
Abstract
We wish to make inferences about the conditional probabilities $p(y|x)$, many of which are zero, when the distribution of X is unknown and one observes only a multinomial sample of the Y variates. To do this, fixed likelihood ratio models and quasi-incremental distributions are defined. It is shown that quasi-incremental distributions are intimately linked to decomposable graphs and that these graphs can guide us to transformations of X and Y which admit a conjugate Bayesian analysis on a reparametrization of the conditional probabilities of interest.
Keywords
62F15, 62H17, Bayesian probability estimation, constraint graph, Contingency tables, decomposable graph, generalized Dirichlet distributions, separation of likelihood
Enable JavaScript for citation tools and additional paper interactions.