A novel viewpoint for Bayesian inversion based on the Poisson point process

Abstract

We present a novel Bayesian framework for inverse problems in which the pos terior distribution is interpreted as the intensity measure of a Poisson point process (PPP). The posterior density is approximated using kernel density estimation, and the superposition property of PPPs is then exploited to enable efficient sampling from each kernel component. This methodology offers a new means of exploring the posterior distribution and facilitates the generation of independent and identically distributed samples, thereby enhancing the analysis of inverse problem solutions.