# Perfect Sampling for Gibbs Point Processes Using Partial Rejection Sampling

## TL;DR

This paper introduces a perfect sampling algorithm for Gibbs point processes, leveraging partial rejection sampling, with efficiency depending on interaction range and point intensity.

## Contribution

It develops a novel perfect sampling method tailored for specific Gibbs point processes with finite interaction range, improving sampling efficiency.

## Key findings

- Expected running time scales as O(log(1/r))
- Algorithm effective for moderate point intensities
- Applicable to pairwise interaction, penetrable spheres, and area-interaction models

## Abstract

We present a perfect sampling algorithm for Gibbs point processes, based on the partial rejection sampling of Guo et al. (2017). Our particular focus is on pairwise interaction processes, penetrable spheres mixture models and area-interaction processes, with a finite interaction range. For an interaction range $2r$ of the target process, the proposed algorithm can generate a perfect sample with $O(\log(1/r))$ expected running time complexity, provided that the intensity of the points is not too high.