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A measure of evidence based on the likelihood-ratio statistics

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Abstract

In this paper, we show that the likelihood-ratio measure (a) is invariant with respect to dominating sigma-finite measures, (b) satisfies logical consequences which are not satisfied by standard p values, (c) respects frequentist properties, i.e., the type I error can be properly controlled, and, under mild regularity conditions, (d) can be used as an upper bound for posterior probabilities. We also discuss a generic application to test whether the genotype frequencies of a given population are under the Hardy–Weinberg equilibrium, under inbreeding restrictions or under outbreeding restrictions.

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Acknowledgements

This work received Grants from FAPESP–Brazil (2014/25595-0) and CNPq (200115/2015-4). This paper was partially developed in the Department of Biochemistry, Microbiology, and Immunology, University of Ottawa, Canada, and in the Department of Statistics, University of São Paulo, Brazil.

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  1. Departamento de Estatística, IME, Universidade de São Paulo, Rua do Matão, 1010, São Paulo, SP, 05508-090, Brazil

    Alexandre Galvão Patriota

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  1. Alexandre Galvão Patriota
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Correspondence to Alexandre Galvão Patriota.

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Patriota, A.G. A measure of evidence based on the likelihood-ratio statistics. Stat Papers 63, 1931–1951 (2022). https://doi.org/10.1007/s00362-022-01301-3

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