2021/05/28 by Francesco Bertolino, Bertolino, Francesco, Mara Manca +7
Decision Sciences · Mathematics · #62A #62C10 #62F03 #62F15 #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Forecasting Techniques and Applications #Methodology (stat.ME) #Scientific Measurement and Uncertainty Evaluation
paper · pdf · doi:10.48550/arxiv.2105.13716
openalex publication_date 2021/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 the BDT with the Full Bayesian Significance Test, a well-known Bayesian testing procedure for sharp hypotheses.