On the Generalization of the Likelihood Function and the Likelihood Principle
- 1 June 1996
- journal article
- research article
- Published by Taylor & Francis in Journal of the American Statistical Association
- Vol. 91 (434) , 791-806
- https://doi.org/10.1080/01621459.1996.10476947
Abstract
The parametric likelihood and likelihood principle (LP) play a central role in parametric methodology and in the foundations of statistics. The main purpose of this article is to extend the concepts of likelihood and LP to general inferential aims and models covering, for example, prediction and empirical Bayes models. The likelihood function is the joint distribution of the data and the unobserved variables of inferential interest, considered as a function of the parameters and these inferential variables. LP is based on this likelihood, and the principles of sufficiency (SP) and conditionality (CP) are modified such that the equivalence SP and CP ⇔ LP is valid, generalizing Birnbaum's theorem.Keywords
This publication has 34 references indexed in Scilit:
- A general framework for model-based statisticsBiometrika, 1990
- The Validity of the Likelihood PrincipleThe American Statistician, 1987
- Models for Nonresponse in Sample SurveysJournal of the American Statistical Association, 1982
- A Note on Birnbaum's Theory of the Likelihood PrincipleJournal of the American Statistical Association, 1976
- More on Concepts of Statistical EvidenceJournal of the American Statistical Association, 1972
- Comments on a Weakened Principle of ConditionalityJournal of the American Statistical Association, 1970
- On Birnbaum's Theorem on the Relation between Sufficiency, Conditionality and LikelihoodJournal of the American Statistical Association, 1970
- On the Foundations of Statistical InferenceJournal of the American Statistical Association, 1962
- Likelihood Inference and Time SeriesJournal of the Royal Statistical Society. Series A (General), 1962
- Some Problems Connected with Statistical InferenceThe Annals of Mathematical Statistics, 1958