Second order semi-parametric inference for multivariate log Gaussian Cox processes

TL;DR

This paper presents a semi-parametric method for inferring second-order properties of multivariate log Gaussian Cox processes, effectively handling complex intensity functions and outperforming existing methods in simulated and real data applications.

Contribution

It introduces a second-order conditional composite likelihood that is independent of the complex intensity part, along with model selection and regularization algorithms.

Findings

Outperforms existing methods in simulated data

Effective in microscopy and criminology data

Provides sparse models for cross pair correlation functions

Abstract

This paper introduces a new approach to inferring the second order properties of a multivariate log Gaussian Cox process (LGCP) with a complex intensity function. We assume a semi-parametric model for the multivariate intensity function containing an unspecified complex factor common to all types of points. Given this model we exploit the availability of several types of points to construct a second-order conditional composite likelihood to infer the pair correlation and cross pair correlation functions of the LGCP. Crucially this likelihood does not depend on the unspecified part of the intensity function. We also introduce a cross validation method for model selection and an algorithm for regularized inference that can be used to obtain sparse models for cross pair correlation functions. The methodology is applied to simulated data as well as data examples from microscopy and criminology. This shows how the new approach outperforms existing alternatives where the intensity functions are estimated non-parametrically.