Autori
Bertolini, Francesco
Ventura, Laura
Racugno, Walter
Musio, Monica
Manca, Mara

Titolo
A new Bayesian discrepancy measure
Periodico
Statistical methods & applications : Journal of the Italian Statistical Society
Anno: 2024 - Volume: 33 - Fascicolo: 2 - Pagina iniziale: 381 - Pagina finale: 405

The aim of this article is to make a contribution to the Bayesian procedure of testing precise hypotheses for parametric models. For this purpose, we define the Bayesian Discrepancy Measure that allows one to evaluate the suitability of a given hypothesis with respect to the available information (prior law and data). To summarise this information, the posterior median is employed, allowing a simple assessment of the discrepancy with a fixed hypothesis. The Bayesian Discrepancy Measure assesses the compatibility of a single hypothesis with the observed data, as opposed to the more common comparative approach where a hypothesis is rejected in favour of a competing hypothesis. The proposed measure of evidence has properties of consistency and invariance. After presenting the definition of the measure for a parameter of interest, both in the absence and in the presence of nuisance parameters, we illustrate some examples showing its conceptual and interpretative simplicity. Finally, we compare a test procedure based on the Bayesian Discrepancy Measure, with the Full Bayesian Significance Test, a well-known Bayesian testing procedure for sharp hypotheses.



SICI: 1618-2510(2024)33:2<381:ANBDM>2.0.ZU;2-Q

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