Quasi-likelihood for Spatial Point Processes

Abstract

Fitting regression models for intensity functions of spatial point processes is of great interest in ecological and epidemiological studies of association between spatially referenced events and geographical or environmental covariates. When Cox or cluster process models are used to accommodate clustering not accounted for by the available covariates, likelihood based inference becomes computationally cumbersome due to the complicated nature of the likelihood function and the associated score function. It is therefore of interest to consider alternative more easily computable estimating functions. We derive the optimal estimating function in a class of first-order estimating functions. The optimal estimating function depends on the solution of a certain Fredholm integral equation which in practice is solved numerically. The approximate solution is equivalent to a quasi-likelihood for binary spatial data and we therefore use the term quasi-likelihood for our optimal estimating function approach. We demonstrate in a simulation study and a data example that our quasi-likelihood method for spatial point processes is both statistically and computationally efficient.

References in corpus (3)

• A toolbox for fitting complex spatial point process models using integrated nested Laplace approximation (INLA)
• Quasi-likelihood for Spatial Point Processes
• Analysis of binary spatial data by quasi-likelihood estimating equations

Cited by in corpus (7)

• Quasi-likelihood for Spatial Point Processes
• Convex and non-convex regularization methods for spatial point processes intensity estimation
• Orthogonal series estimation of the pair correlation function of a spatial point process
• Quick inference for log Gaussian Cox processes with non-stationary underlying random fields
• Regularization techniques for inhomogeneous (spatial) point processes intensity and conditional intensity estimation
• Multivariate Temporal Point Process Regression
• Fused Spatial Point Process Intensity Estimation with Varying Coefficients on Complex Constrained Domains