Bayesian Discrepancy Measure: Higher-Order and Skewed Approximations
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 univariat...
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MDPI AG
2025-06-01
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| Online Access: | https://www.mdpi.com/1099-4300/27/7/657 |
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| author | Elena Bortolato Francesco Bertolino Monica Musio Laura Ventura |
| author_facet | Elena Bortolato Francesco Bertolino Monica Musio Laura Ventura |
| author_sort | Elena Bortolato |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-59317e48593f44d8aeafaef5d1b3bf80 |
| institution | Kabale University |
| issn | 1099-4300 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj-art-59317e48593f44d8aeafaef5d1b3bf802025-08-20T03:58:27ZengMDPI AGEntropy1099-43002025-06-0127765710.3390/e27070657Bayesian Discrepancy Measure: Higher-Order and Skewed ApproximationsElena Bortolato0Francesco Bertolino1Monica Musio2Laura Ventura3Barcelona School of Economics, Universitat Pompeu Fabra, 08005 Barcelona, SpainDepartment of Mathematics and Computer Science, University of Cagliari, 09124 Cagliari, ItalyDepartment of Mathematics and Computer Science, University of Cagliari, 09124 Cagliari, ItalyDepartment of Statistical Sciences, University of Padova, 35121 Padova, ItalyThe 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.https://www.mdpi.com/1099-4300/27/7/657Bayesian discrepancy measurecredible regionsevidencehigher-order asymptoticsmatching priorsnuisance parameter |
| spellingShingle | Elena Bortolato Francesco Bertolino Monica Musio Laura Ventura Bayesian Discrepancy Measure: Higher-Order and Skewed Approximations Entropy Bayesian discrepancy measure credible regions evidence higher-order asymptotics matching priors nuisance parameter |
| title | Bayesian Discrepancy Measure: Higher-Order and Skewed Approximations |
| title_full | Bayesian Discrepancy Measure: Higher-Order and Skewed Approximations |
| title_fullStr | Bayesian Discrepancy Measure: Higher-Order and Skewed Approximations |
| title_full_unstemmed | Bayesian Discrepancy Measure: Higher-Order and Skewed Approximations |
| title_short | Bayesian Discrepancy Measure: Higher-Order and Skewed Approximations |
| title_sort | bayesian discrepancy measure higher order and skewed approximations |
| topic | Bayesian discrepancy measure credible regions evidence higher-order asymptotics matching priors nuisance parameter |
| url | https://www.mdpi.com/1099-4300/27/7/657 |
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