Bayesian Monte Carlo testing with one-dimensional measures of evidence.
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2019
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Resumo
Bayesian hypothesis testing procedures are constructed by means of test statistics which
are functions of the posterior distribution. Usually, the whole sample vector is selected to
form the sufficient empirical part of the posterior distribution. But, in certain problems,
one may prefer to use well-established one-dimensional sufficient statistics in place of the
sample vector. This paper introduces a Bayesian Monte Carlo procedure specially designed
for such cases. It is shown that the performance of this new approach is arbitrarily close
to the exact Bayesian test. In addition, for arbitrary desired precisions, we develop a theoretical
rule of thumb for choosing the minimum number m0 of Monte Carlo simulations.
Surprisingly, m0 does not depend on the shape of loss/cost functions when those are used
to compound the test statistic. The method is illustrated for testing mean vectors in highdimension
and for detecting spatial clusters of diseases in aggregated maps.
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Bayes factor, Expected loss, Exact test
Citação
SILVA, I. R.; MARQUES, R. A. G. Bayesian Monte Carlo testing with one-dimensional measures of evidence. Journal of Computational and Applied Mathematics, v. 351, p. 250-259, maio 2018. Disponível em: <https://www.sciencedirect.com/science/article/pii/S0377042718306964>. Acesso em: 19 mar. 2019.