# Exact Bayesian Gaussian Cox Processes Using Random Integral

arXiv: https://arxiv.org/abs/2406.19722 · HTML: https://mlsanity.com/paper/2406.19722/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 39 references that are in the map.
- First posted on arXiv 28 Jun 2024.

## Builds on (most cited first, 9 of 9)

- [Neural Spatio-Temporal Point Processes](https://mlsanity.com/paper/2011.04583/) (2020)
- [Variational Inference for Gaussian Process Modulated Poisson Processes](https://mlsanity.com/paper/1411.0254/) (2014)
- [Efficient Bayesian Inference of Sigmoidal Gaussian Cox Processes](https://mlsanity.com/paper/1808.00831/) (2018)
- [Spatial and Spatio-Temporal Log-Gaussian Cox Processes: Extending the Geostatistical Paradigm](https://mlsanity.com/paper/1312.6536/) (2013)
- [Gaussian Processes for Survival Analysis](https://mlsanity.com/paper/1611.00817/) (2016)
- [Structured Variational Inference in Continuous Cox Process Models](https://mlsanity.com/paper/1906.03161/) (2019)
- [Scalable Nonparametric Bayesian Inference on Point Processes with Gaussian Processes](https://mlsanity.com/paper/1410.6834/) (2014)
- [Gaussian Process Modulated Cox Processes under Linear Inequality Constraints](https://mlsanity.com/paper/1902.10974/) (2019)
- [Gaussian process regression for survival data with competing risks](https://mlsanity.com/paper/1312.1591/) (2013)

## Abstract (arXiv)

A Gaussian Cox process is a popular model for point process data, in which the intensity function is a transformation of a Gaussian process. Posterior inference of this intensity function involves an intractable integral (i.e., the cumulative intensity function) in the likelihood resulting in doubly intractable posterior distribution. Here, we propose a nonparametric Bayesian approach for estimating the intensity function of an inhomogeneous Poisson process without reliance on large data augmentation or approximations of the likelihood function. We propose to jointly model the intensity and the cumulative intensity function as a transformed Gaussian process, allowing us to directly bypass the need of approximating the cumulative intensity function in the likelihood. We propose an exact MCMC sampler for posterior inference and evaluate its performance on simulated data. We demonstrate the utility of our method in three real-world scenarios including temporal and spatial event data, as well as aggregated time count data collected at multiple resolutions. Finally, we discuss extensions of our proposed method to other point processes.