Properly constrained reference priors decay rates for efficient and robust posterior inference

2024/09/19 by Antoine Van Biesbroeck, Van Biesbroeck, Antoine
Engineering · #FOS: Computer and information sciences #FOS: Mathematics #Fault Detection and Control Systems #Geophysical Methods and Applications #Methodology (stat.ME) #Sparse and Compressive Sensing Techniques #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2409.13041

openalex publication_date 2024/09/19 · openalex created_date 2024/10/26 · openalex updated_date 2026/07/28

Abstract

In Bayesian analysis, reference priors are widely recognized for their objective nature. Yet, they often lead to intractable and improper priors, which complicates their application. Besides, informed prior elicitation methods are penalized by the subjectivity of the choices they require. In this paper, we aim at proposing a reconciliation of the aforementioned aspects. Leveraging the objective aspect of reference prior theory, we introduce two strategies of constraint incorporation to build tractable reference priors. One provides a simple and easy-to-compute solution when the improper aspect is not questioned, and the other introduces constraints to ensure the reference prior is proper, or it provides proper posterior. Our methodology emphasizes the central role of Jeffreys prior decay rates in this process, and the practical applicability of our results is demonstrated using an example taken from the literature.

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