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Upper probabilities based only on the likelihood function
Author(s) -
Walley P.,
Moral S.
Publication year - 1999
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00205
Subject(s) - frequentist inference , likelihood function , fiducial inference , statistical inference , inference , mathematics , likelihood principle , nuisance parameter , function (biology) , parametric statistics , consistency (knowledge bases) , bayesian inference , statistics , computer science , artificial intelligence , bayesian probability , estimation theory , discrete mathematics , estimator , quasi maximum likelihood , evolutionary biology , biology
In the problem of parametric statistical inference with a finite parameter space, we propose some simple rules for defining posterior upper and lower probabilities directly from the observed likelihood function, without using any prior information. The rules satisfy the likelihood principle and a basic consistency principle (‘avoiding sure loss’), they produce vacuous inferences when the likelihood function is constant, and they have other symmetry, monotonicity and continuity properties. One of the rules also satisfies fundamental frequentist principles. The rules can be used to eliminate nuisance parameters, and to interpret the likelihood function and to use it in making decisions. To compare the rules, they are applied to the problem of sampling from a finite population. Our results indicate that there are objective statistical methods which can reconcile three general approaches to statistical inference: likelihood inference, coherent inference and frequentist inference.