Work

Bayesian Discrepancy Measure: Higher-Order and Skewed Approximations

Year: 2025

Type: article

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.

Source: Entropy

DOI: 10.3390/e27070657

Authors: Elena Bortolato, Francesco Bertolino, Monica Musio, Laura Ventura

Institutions: Universitat Pompeu Fabra, Barcelona School of Economics, University of Cagliari, University of Padua

Language: English

Topic: Statistical Methods and Bayesian Inference

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funders: European Commission, H2020 European Research Council