Translator Disclaimer
February, 1970 The Weighted Likelihood Ratio, Sharp Hypotheses about Chances, the Order of a Markov Chain
James M. Dickey, B. P. Lientz
Ann. Math. Statist. 41(1): 214-226 (February, 1970). DOI: 10.1214/aoms/1177697203

Abstract

The Bayesian theory for testing a sharp hypothesis, defined by fixed values of parameters, is here presented in general terms. Arbitrary positive prior probability is attached to the hypothesis. The ratio of posterior to prior odds for the hypothesis is given by the weighted likelihood ratio, shown here to equal Leonard J. Savage's (1963) ratio of a posterior to a prior density (2.21). This Bayesian approach to hypothesis testing was suggested by Jeffreys (1948), Savage (1959), (1961), Lindley (1961), and Good (1950), (1965), but obscured some what by approximations and unique choices of prior distributions. This Bayesian theory is distinct from that of Lindley (1965) and that of Dickey (1967a). Applications are given to hypotheses about multinomial means, for example, equality of two binomial probabilities. A new test is presented for the order of a finite-state Markov chain.

Citation

Download Citation

James M. Dickey. B. P. Lientz. "The Weighted Likelihood Ratio, Sharp Hypotheses about Chances, the Order of a Markov Chain." Ann. Math. Statist. 41 (1) 214 - 226, February, 1970. https://doi.org/10.1214/aoms/1177697203

Information

Published: February, 1970
First available in Project Euclid: 27 April 2007

zbMATH: 0188.50102
MathSciNet: MR258187
Digital Object Identifier: 10.1214/aoms/1177697203

Rights: Copyright © 1970 Institute of Mathematical Statistics

JOURNAL ARTICLE
13 PAGES


SHARE
Vol.41 • No. 1 • February, 1970
Back to Top