## The Annals of Statistics

- Ann. Statist.
- Volume 4, Number 6 (1976), 1159-1189.

### On the Application of Symmetric Dirichlet Distributions and their Mixtures to Contingency Tables

#### Abstract

Bayes factors against various hypotheses of independence are proposed for contingency tables and for multidimensional contingency tables. The priors assumed for the nonnull hypothesis are linear combinations of symmetric Dirichlet distributions as in some work of 1965 and later. The results can be used also for probability estimation. The evidence concerning independence, provided by the marginal totals alone, is evaluated, and preliminary numerical calculations suggest it is small. The possibility of applying the Bayes/non-Bayes synthesis is proposed because it was found useful for an analogous problem for multinomial distributions. As a spinoff, approximate formulae are suggested for enumerating "arrays" in two and more dimensions.

#### Article information

**Source**

Ann. Statist. Volume 4, Number 6 (1976), 1159-1189.

**Dates**

First available in Project Euclid: 12 April 2007

**Permanent link to this document**

http://projecteuclid.org/euclid.aos/1176343649

**Digital Object Identifier**

doi:10.1214/aos/1176343649

**Mathematical Reviews number (MathSciNet)**

MR428568

**Zentralblatt MATH identifier**

0348.62018

**JSTOR**

links.jstor.org

**Subjects**

Primary: 62F15: Bayesian inference

Secondary: 62G10: Hypothesis testing 05A15: Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx]

**Keywords**

Contingency tables multidimensional contingency tables combinations of Dirichlet distributions Bayes factor Bayes/non-Bayes synthesis enumeration of arrays independence multidimensional asymptotic expansions

#### Citation

Good, I. J. On the Application of Symmetric Dirichlet Distributions and their Mixtures to Contingency Tables. Ann. Statist. 4 (1976), no. 6, 1159--1189. doi:10.1214/aos/1176343649. http://projecteuclid.org/euclid.aos/1176343649.

#### See also

- Part II: J. F. Crook, I. J. Good. On the Application of Symmetric Dirichlet Distributions and Their Mixtures to Contingency Tables, Part II. Ann. Statist., Volume 8, Number 6 (1980), 1198--1218.Project Euclid: euclid.aos/1176345194

#### Corrections

- See Correction: J. F. Crook, I. J. Good. Corrections to "On the Application of Symmetric Dirichlet Distributions and Their Mixtures to Contingency Tables, Part II". Ann. Statist., Volume 9, Number 5 (1981), 1133--1133.Project Euclid: euclid.aos/1176345597