Using smoothers for fast, flexible fits to log-Gaussian Cox process models and their multivariate extensions

Abstract

 Log-Gaussian Cox processes are a useful framework for modelling spatial point patterns since the latent field can capture spatial correlation unaccounted for by measured predictors. However, fitting these models can be challenging – both in terms of computational efficiency, and the degree to which bespoke software is required. In this seminar, I will talk about my efforts to counter these challenges and how doing so permits novel ways of analysing these data.

Our approach to fitting a log-Gaussian Cox process optimises the approximate marginal likelihood using a combination of automatic differentiation and spatial basis functions to approximate the latent field. Additionally, by considering the basis expansion as a smoother over the domain, we can fit this type of model using generalised additive modelling or mixed modelling software – easing the technological barrier for applied researchers wanting to fit log-Gaussian Cox processes. We find that these approaches achieve comparable fits to state-of-the-art software, often more efficiently. This efficiency enables us to explore multivariate extensions - we additionally take a factor-analytic approximation to the multivariate latent field (via the basis coefficients) to capture correlation between point types. This model was implemented using glmmTMB, a widely used mixed modelling package on R, and was used to construct a biplot to concisely visualise co-occurrence of points in multiple, correlated spatial point patterns.