# Spatial and Spatio-Temporal Log-Gaussian Cox Processes: Extending the Geostatistical Paradigm

arXiv: https://arxiv.org/abs/1312.6536 · HTML: https://mlsanity.com/paper/1312.6536/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Dec 2013.

## Built on by (most cited first, 14 of 14)

- [Bayesian Optimization through Gaussian Cox Process Models for Spatio-temporal Data](https://mlsanity.com/paper/2401.14544/) (2024)
- [Sensing Cox Processes via Posterior Sampling and Positive Bases](https://mlsanity.com/paper/2110.11181/) (2021)
- [Active learning-assisted neutron spectroscopy with log-Gaussian processes](https://mlsanity.com/paper/2209.00980/) (2022)
- [Multi-fidelity Monte Carlo: a pseudo-marginal approach](https://mlsanity.com/paper/2210.01534/) (2022)
- [Heterogeneous Multi-Task Gaussian Cox Processes](https://mlsanity.com/paper/2308.15364/) (2023)
- [Understanding the Spread of COVID-19 Epidemic: A Spatio-Temporal Point Process View](https://mlsanity.com/paper/2106.13097/) (2021)
- [Cox-Hawkes: doubly stochastic spatiotemporal Poisson processes](https://mlsanity.com/paper/2210.11844/) (2022)
- [Semi-Parametric Inference for Doubly Stochastic Spatial Point Processes: An Approximate Penalized Poisson Likelihood Approach](https://mlsanity.com/paper/2306.06756/) (2023)
- [Exact Bayesian Gaussian Cox Processes Using Random Integral](https://mlsanity.com/paper/2406.19722/) (2024)
- [DeepRV: Accelerating Spatiotemporal Inference with Pre-trained Neural Priors](https://mlsanity.com/paper/2503.21473/) (2025)
- [K2IE: Kernel Method-based Kernel Intensity Estimators for Inhomogeneous Poisson Processes](https://mlsanity.com/paper/2505.24704/) (2025)
- [Hybrid Belief Reinforcement Learning for Efficient Coordinated Spatial Exploration](https://mlsanity.com/paper/2603.03595/) (2026)
- [When Context Compensates for Sparse Event History: AlphaEarth for Spatio-Temporal Point-Process Forecasting](https://mlsanity.com/paper/2607.01082/) (2026)
- [Scalable Sparse Autoregressive Variational Inference for Non-Gaussian Spatial Fields](https://mlsanity.com/paper/2610.13656/) (2026)

## Abstract (arXiv)

In this paper we first describe the class of log-Gaussian Cox processes (LGCPs) as models for spatial and spatio-temporal point process data. We discuss inference, with a particular focus on the computational challenges of likelihood-based inference. We then demonstrate the usefulness of the LGCP by describing four applications: estimating the intensity surface of a spatial point process; investigating spatial segregation in a multi-type process; constructing spatially continuous maps of disease risk from spatially discrete data; and real-time health surveillance. We argue that problems of this kind fit naturally into the realm of geostatistics, which traditionally is defined as the study of spatially continuous processes using spatially discrete observations at a finite number of locations. We suggest that a more useful definition of geostatistics is by the class of scientific problems that it addresses, rather than by particular models or data formats.