Statistical Decisions Using Likelihood Information Without Prior Probabilities

This paper presents a decision-theoretic approach to statistical inference that satisfies the Likelihood Principle (LP) without using prior information. Unlike the Bayesian approach, which also satisfies LP, we do not assume knowledge of the prior distribution of the unknown parameter. With respect to information that can be obtained from an experiment, our solution is more efficient than Wald's minimax solution. However, with respect to information assumed to be known before the experiment, our solution demands less input than the Bayesian solution.

[1]  E. S. Pearson,et al.  ON THE USE AND INTERPRETATION OF CERTAIN TEST CRITERIA FOR PURPOSES OF STATISTICAL INFERENCE PART I , 1928 .

[2]  Koichi Miyasawa,et al.  On the statistical decision function I. , 1950 .

[3]  Abraham Wald,et al.  Statistical Decision Functions , 1951 .

[4]  Howard Raiffa,et al.  Games And Decisions , 1958 .

[5]  E. Lehmann.  Testing Statistical Hypotheses , 1960 .

[6]  W. D. Ray.  The Foundation of Statistical Inference , 1963 .

[7]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[8]  Pranab Kumar Sen,et al.  Asymptotic Optimality of Likelihood Ratio Tests in Exponential Families , 1980 .

[9]  V. Barnett,et al.  Comparative Statistical Inference (2nd ed.). , 1983 .

[10]  J. Werther.  D. Geldart (Ed.): Gas Fluidization Technology, John Wiley & Sons. Chichester, New York, Brisbane, Toronto, Singapore 1986. 468 Seiten, Preis: £ 42.50 , 1987 .

[11]  J. K. Ghosh,et al.  Statistical information and likelihood : a collection of critical essays , 1989 .

[12]  Ronald Fagin,et al.  Two Views of Belief: Belief as Generalized Probability and Belief as Evidence , 1992, Artif. Intell..

[13]  H. Levy.  Stochastic dominance and expected utility: survey and analysis , 1992 .

[14]  D. Dubois,et al.  A Semantics for Possibility Theory Based on Likelihoods , 1997 .

[15]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[16]  Hung T. Nguyen,et al.  Possibility Theory, Probability and Fuzzy Sets Misunderstandings, Bridges and Gaps , 2000 .

[17]  Phan Hong Giang,et al.  A Qualitative Linear Utility Theory for Spohn's Theory of Epistemic Beliefs , 2000, UAI.

[18]  Vic Barnett,et al.  Comparative Statistical Inference , 1974, Technometrics.

[19]  T. Severini.  Likelihood Methods in Statistics , 2001 .

[20]  Phan Hong Giang,et al.  A Comparison of Axiomatic Approaches to Qualitative Decision Making Using Possibility Theory , 2001, UAI.