The Annals of Mathematical Statistics

The Bayesian Analysis of Contingency Tables

Dennis V. Lindley

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Abstract

This paper describes how data from a multinomial distribution, and in particular data in the form of a contingency table, may be studied by using a prior distribution of the parameters and expressing the results in the form of a posterior distribution, or some aspects thereof, of the parameters. The analysis used must depend on the prior distribution and the form described here only applies to a certain type of prior knowledge but, for reasons given below, it is believed that this type is of frequent occurrence. The binomial situation is first considered and the results obtained there suggest a general result for the multinomial distribution, which is then established. A few remarks on Bayesian analysis in general enable the result to be applied, first to certain multinomial problems and then, with the aid of another general result, to contingency tables. The method used there has close connections with the Analysis of Variance and these connections are examined, particularly with a view to simplifying the analysis of contingency tables involving three or more factors.

Article information

Source
Ann. Math. Statist., Volume 35, Number 4 (1964), 1622-1643.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177700386

Digital Object Identifier
doi:10.1214/aoms/1177700386

Mathematical Reviews number (MathSciNet)
MR166885

Zentralblatt MATH identifier
0134.37101

JSTOR
links.jstor.org

Citation

Lindley, Dennis V. The Bayesian Analysis of Contingency Tables. Ann. Math. Statist. 35 (1964), no. 4, 1622--1643. doi:10.1214/aoms/1177700386. https://projecteuclid.org/euclid.aoms/1177700386


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