[Paper Review] lgcp An R Package for Inference with Spatio-Temporal Log-Gaussian Cox Processes

Benjamín M. Taylor, Tilman M. Davies+2 more|arXiv (Cornell University)|Oct 27, 2011

Markov Chains and Monte Carlo Methods22 references3 citations

TL;DR

This paper introduces the lgcp R package for inference with spatio-temporal log-Gaussian Cox processes, enabling real-time predictive modeling of point event data using Markov chain Monte Carlo (MCMC) methods. The key contribution is a flexible, extensible framework for spatio-temporal prediction, including efficient data rotation to improve MCMC efficiency and integration with established R packages for spatial statistics and covariance modeling.

ABSTRACT

This paper introduces an R package for spatio-temporal prediction and forecasting for log-Gaussian Cox processes. The main computational tool for these models is Markov chain Monte Carlo and the new package, lgcp, therefore also provides an extensible suite of functions for implementing MCMC algorithms for processes of this type. The modelling framework and details of inferential procedures are first presented before a tour of lgcp functionality is given via a walk-through data-analysis. Topics covered include reading in and converting data, estimation of the key components and parameters of the model, specifying output and simulation quantities, computation of Monte Carlo expectations, post-processing and simulation of data sets.

Motivation & Objective

• To develop an R package for statistical inference in spatio-temporal log-Gaussian Cox processes, particularly for disease surveillance applications.
• To provide a computationally efficient framework for real-time predictive inference using MCMC sampling.
• To improve MCMC efficiency through automatic rotation of observation windows to align with the grid structure.
• To integrate seamlessly with existing R packages such as spatstat, RandomFields, and sp for data handling and covariance modeling.
• To support simulation, parameter estimation, and post-processing of predictive distributions for spatio-temporal intensity forecasting.

Proposed method

• Models spatio-temporal point process intensity as $ R(x,t) = \lambda(s)\mu(t)\exp\{\mathcal{Y}(x,t)\} $, where $ \mathcal{Y} $ is a second-order stationary Gaussian process.
• Employs a covariance structure $ \mathrm{cov}[\mathcal{Y}(s_1,t_1), \mathcal{Y}(s_2,t_2)] = \sigma^2 r(\|s_2-s_1\|; \phi) \exp\{-\theta|t_2-t_1|\} $, capturing space-time dependence.
• Uses Markov chain Monte Carlo (MCMC) for posterior inference, with a Metropolis-within-Gibbs algorithm implemented via the package’s core functions.
• Introduces automatic window rotation to minimize the number of FFT grid cells, improving MCMC efficiency without affecting computational speed.
• Provides functions for data input, model fitting, prediction, simulation, and post-processing using standard R data structures and packages.
• Leverages external packages: spatstat for point process handling, RandomFields for covariance functions, and ncdf for efficient I/O on large datasets.

Experimental results

Research questions

• RQ1 How can spatio-temporal log-Gaussian Cox processes be efficiently inferred in real-time for disease surveillance applications?
• RQ2 What is the impact of observation window orientation on MCMC efficiency in spatio-temporal point process models?
• RQ3 How can existing R packages for spatial statistics be integrated into a unified framework for spatio-temporal inference?
• RQ4 What are the computational and statistical trade-offs of using rotated grids in MCMC sampling for log-Gaussian Cox processes?
• RQ5 How can predictive distributions of future intensity be efficiently computed and visualized for risk assessment?

Key findings

• The lgcp package enables real-time predictive inference for spatio-temporal log-Gaussian Cox processes using MCMC, with support for forecasting intensity at future locations and times.
• Automatic window rotation can reduce the number of FFT grid cells by up to 200%, significantly improving MCMC efficiency without altering computational speed.
• The package achieves a 200% efficiency gain in grid cell usage when rotation is applied, as demonstrated in the example with a non-rectangular observation window.
• The package supports flexible data input through conversion methods for spatstat, sp, and sparr objects, enabling seamless integration with diverse data formats.
• The lgcpSim function allows approximate simulation of spatio-temporal point processes using user-defined spatial and temporal intensity functions and model parameters.
• Predictions from lgcpPredict are returned in the rotated coordinate system if rotation is applied, requiring post-processing for alignment with original spatial axes.