Bayesian discrepancy measure: higher-order and skewed approximations

Mostra el registre complet Registre parcial de l'ítem

• dc.contributor.author Bortolato, Elena
• dc.contributor.author Bertolino, Francesco
• dc.contributor.author Musio, Monica
• dc.contributor.author Ventura, Laura
• dc.date.accessioned 2025-09-08T10:48:37Z
• dc.date.available 2025-09-08T10:48:37Z
• dc.date.issued 2025
• dc.description.abstract The aim of this paper is to discuss both higher-order asymptotic expansions and skewed approximations for the Bayesian discrepancy measure used in testing precise statistical hypotheses. In particular, we derive results on third-order asymptotic approximations and skewed approximations for univariate posterior distributions, including cases with nuisance parameters, demonstrating improved accuracy in capturing posterior shape with little additional computational cost over simple first-order approximations. For third-order approximations, connections to frequentist inference via matching priors are highlighted. Moreover, the definition of the Bayesian discrepancy measure and the proposed methodology are extended to the multivariate setting, employing tractable skew-normal posterior approximations obtained via derivative matching at the mode. Accurate multivariate approximations for the Bayesian discrepancy measure are then derived by defining credible regions based on an optimal transport map that transforms the skew-normal approximation to a standard multivariate normal distribution. The performance and practical benefits of these higher-order and skewed approximations are illustrated through two examples.en
• dc.description.sponsorship Elena Bortolato acknowledges funding from the European Union under the ERC grant project number 864863.en
• dc.format.mimetype application/pdf
• dc.identifier.citation Bortolato E, Bertolino F, Musio M, Ventura L. Bayesian discrepancy measure: higher-order and skewed approximations. Entropy. 2025 Jul;27(7):657. DOI: 10.3390/e27070657
• dc.identifier.doi http://dx.doi.org/10.3390/e27070657
• dc.identifier.issn 1099-4300
• dc.identifier.uri http://hdl.handle.net/10230/71143
• dc.language.iso eng
• dc.publisher MDPI
• dc.relation.ispartof Entropy. 2025 Jul;27(7):657
• dc.relation.projectID info:eu-repo/grantAgreement/EC/FP7/864863
• dc.rights © 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.rights.uri http://creativecommons.org/licenses/by/4.0/
• dc.subject.keyword Bayesian discrepancy measureen
• dc.subject.keyword Credible regionsen
• dc.subject.keyword Evidenceen
• dc.subject.keyword Higher-order asymptoticsen
• dc.subject.keyword Matching priorsen
• dc.subject.keyword Nuisance parameteren
• dc.subject.keyword Optimal transport mapen
• dc.subject.keyword Precise null hypothesisen
• dc.subject.keyword Skewed approximationsen
• dc.subject.keyword Skew-normal distributionen
• dc.subject.keyword Tail area probabilityen
• dc.title Bayesian discrepancy measure: higher-order and skewed approximationsen
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/publishedVersion