# Efficient Bayesian Inference of Sigmoidal Gaussian Cox Processes

arXiv: https://arxiv.org/abs/1808.00831 · HTML: https://mlsanity.com/paper/1808.00831/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Aug 2018.

## Built on by (most cited first, 17 of 17)

- [Learning Density Distribution of Reachable States for Autonomous Systems](https://mlsanity.com/paper/2109.06728/) (2021)
- [Deep Neyman-Scott Processes](https://mlsanity.com/paper/2111.03949/) (2021)
- [Bayesian Optimization through Gaussian Cox Process Models for Spatio-temporal Data](https://mlsanity.com/paper/2401.14544/) (2024)
- [NeuralSurv: Deep Survival Analysis with Bayesian Uncertainty Quantification](https://mlsanity.com/paper/2505.11054/) (2025)
- [Sensing Cox Processes via Posterior Sampling and Positive Bases](https://mlsanity.com/paper/2110.11181/) (2021)
- [Heterogeneous Multi-Task Gaussian Cox Processes](https://mlsanity.com/paper/2308.15364/) (2023)
- [Federated Neural Nonparametric Point Processes](https://mlsanity.com/paper/2410.05637/) (2024)
- [Advances in Temporal Point Processes: Bayesian, Neural, and LLM Approaches](https://mlsanity.com/paper/2501.14291/) (2025)
- [Conjugate Bayesian Two-step Change Point Detection for Hawkes Process](https://mlsanity.com/paper/2409.17591/) (2024)
- [Nonstationary Sparse Spectral Permanental Process](https://mlsanity.com/paper/2410.03581/) (2024)
- [Nonlinear Hawkes Process with Gaussian Process Self Effects](https://mlsanity.com/paper/2105.09618/) (2021)
- [Case Studies for Computing Density of Reachable States for Safe Autonomous Motion Planning](https://mlsanity.com/paper/2209.08073/) (2022)
- [Neural Diffusion Intensity Models for Point Process Data](https://mlsanity.com/paper/2602.24083/) (2026)
- [Scalable and adaptive variational Bayes methods for Hawkes processes](https://mlsanity.com/paper/2212.00293/) (2022)
- [Exact Bayesian Gaussian Cox Processes Using Random Integral](https://mlsanity.com/paper/2406.19722/) (2024)
- [K2IE: Kernel Method-based Kernel Intensity Estimators for Inhomogeneous Poisson Processes](https://mlsanity.com/paper/2505.24704/) (2025)
- [Amortized Variational Inference of Latent Intensities from Replicated Point Patterns](https://mlsanity.com/paper/2610.16669/) (2026)

## Abstract (arXiv)

We present an approximate Bayesian inference approach for estimating the intensity of an inhomogeneous Poisson process, where the intensity function is modelled using a Gaussian process (GP) prior via a sigmoid link function. Augmenting the model using a latent marked Poisson process and P'olya--Gamma random variables we obtain a representation of the likelihood which is conjugate to the GP prior. We estimate the posterior using a variational free--form mean field optimisation together with the framework of sparse GPs. Furthermore, as alternative approximation we suggest a sparse Laplace's method for the posterior, for which an efficient expectation--maximisation algorithm is derived to find the posterior's mode. Both algorithms compare well against exact inference obtained by a Markov Chain Monte Carlo sampler and standard variational Gauss approach solving the same model, while being one order of magnitude faster. Furthermore, the performance and speed of our method is competitive with that of another recently proposed Poisson process model based on a quadratic link function, while not being limited to GPs with squared exponential kernels and rectangular domains.