Quasi-likelihood for Spatial Point Processes

TL;DR

This paper introduces a quasi-likelihood approach for spatial point processes that simplifies inference for complex models, demonstrating efficiency through simulations and real data applications.

Contribution

It develops an optimal estimating function based on a Fredholm integral equation, offering a computationally feasible alternative to likelihood-based inference for spatial point processes.

Findings

Method is statistically efficient

Approach is computationally efficient

Effective in ecological and epidemiological data analysis

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.