Strong maximum a posteriori estimation in Banach spaces with Gaussian priors

2023/04/26 by Hefin Lambley, Lambley, Hefin · 1 citation
Computer Science · Mathematics · #28C20 #60B11 #62F10 #62F15 #62G05 #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2304.13622

openalex publication_date 2023/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article shows that a large class of posterior measures that are absolutely continuous with respect to a Gaussian prior have strong maximum a posteriori estimators in the sense of Dashti et al. (2013). This result holds in any separable Banach space and applies in particular to nonparametric Bayesian inverse problems with additive noise. When applied to Bayesian inverse problems, this significantly extends existing results on maximum a posteriori estimators by relaxing the conditions on the log-likelihood and on the space in which the inverse problem is set.

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