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Objective Priors for Invariant e-Values in the Presence of Nuisance Parameters
Version 1
: Received: 30 November 2023 / Approved: 5 December 2023 / Online: 5 December 2023 (14:10:03 CET)
A peer-reviewed article of this Preprint also exists.
Bortolato, E.; Ventura, L. Objective Priors for Invariant e-Values in the Presence of Nuisance Parameters. Entropy 2024, 26, 58. Bortolato, E.; Ventura, L. Objective Priors for Invariant e-Values in the Presence of Nuisance Parameters. Entropy 2024, 26, 58.
Abstract
This paper aims to contribute to refining the e-values for testing precise hypotheses, especially when dealing with nuisance parameters, leveraging the effectiveness of asymptotic expansions of the posterior. The proposed approach offers the advantage of bypassing the need for elicitation of priors and reference functions for the nuisance parameters and the multidimensional integration step. For this purpose, starting from a Laplace approximation, a posterior distribution for the parameter of interest only is considered and then a suitable objective matching prior is introduced, ensuring that the posterior mode aligns with an equivariant frequentist estimator. Consequently, both Highest Probability Density credible sets and the e-value remain invariant. Some targeted and challenging examples are discussed.
Keywords
Asymptotic expansions; Adjusted score function; Bias reduction; Evidence; Full Bayesian Significance test; Higher-Order asymptotics; Matching priors; Median bias reduction
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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