BART-based inference for Poisson processes

TL;DR

This paper introduces a BART-based Bayesian method for non-parametric inference of Poisson process intensities, enabling full posterior estimation and demonstrating superior performance in simulations and real data applications.

Contribution

It presents a novel BART-based framework for Poisson intensity estimation that allows full Bayesian posterior inference, extending BART's applicability to point process analysis.

Findings

Outperforms existing methods in simulation studies

Effective in high-dimensional settings up to five dimensions

Provides full Bayesian posterior inference for Poisson intensities

Abstract

The effectiveness of Bayesian Additive Regression Trees (BART) has been demonstrated in a variety of contexts including non-parametric regression and classification. A BART scheme for estimating the intensity of inhomogeneous Poisson processes is introduced. Poisson intensity estimation is a vital task in various applications including medical imaging, astrophysics and network traffic analysis. The new approach enables full posterior inference of the intensity in a non-parametric regression setting. The performance of the novel scheme is demonstrated through simulation studies on synthetic and real datasets up to five dimensions, and the new scheme is compared with alternative approaches.