## The Annals of Statistics

### Bayesian models for sparse probability tables

#### 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.

#### Article information

Source
Ann. Statist., Volume 24, Number 5 (1996), 2178-2198.

Dates
First available in Project Euclid: 20 November 2003

https://projecteuclid.org/euclid.aos/1069362316

Digital Object Identifier
doi:10.1214/aos/1069362316

Mathematical Reviews number (MathSciNet)
MR1421167

Zentralblatt MATH identifier
0867.62015

Subjects
Primary: 62F15: Bayesian inference
Secondary: 62H17: Contingency tables

#### Citation

Smith, Jim Q.; Queen, Catriona M. Bayesian models for sparse probability tables. Ann. Statist. 24 (1996), no. 5, 2178--2198. doi:10.1214/aos/1069362316. https://projecteuclid.org/euclid.aos/1069362316