A note on non-parametric Bayesian estimation for Poisson point processes

TL;DR

This paper derives the rate at which Bayesian methods estimate the intensity function of a Poisson point process, providing theoretical insights into the convergence behavior of non-parametric Bayesian estimators.

Contribution

It introduces the posterior contraction rate for non-parametric Bayesian estimation of Poisson process intensities, advancing theoretical understanding.

Findings

Established the posterior contraction rate for the model

Provided theoretical guarantees for Bayesian estimators

Enhanced understanding of Bayesian inference for Poisson processes

Abstract

We derive the posterior contraction rate for non-parametric Bayesian estimation of the intensity function of a Poisson point process.