2023/12/15 by Michiko Okudo, Okudo, Michiko, Keisuke Yano +1
Computer Science · Mathematics · #Advanced Statistical Methods and Models #Bayesian Modeling and Causal Inference #FOS: Mathematics #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2312.09586
openalex publication_date 2023/12/15 · openalex created_date 2023/12/19 · openalex updated_date 2026/07/28
Bayesian statistics has two common measures of central tendency of a posterior distribution: posterior means and Maximum A Posteriori (MAP) estimates. In this paper, we discuss a connection between MAP estimates and posterior means. We derive an asymptotic condition for a pair of prior densities under which the posterior mean based on one prior coincides with the MAP estimate based on the other prior. A sufficient condition for the existence of this prior pair relates to α-flatness of the statistical model in information geometry. We also construct a matching prior pair using α-parallel priors. Our result elucidates an interesting connection between regularization in generalized linear regression models and posterior expectation.