Abstract
Log-Gaussian Cox processes are an important class of models for spatial and spatiotemporal point-pattern data. Delivering robust Bayesian inference for this class of models presents a substantial challenge, since Markov chain Monte Carlo (MCMC) algorithms require careful tuning in order to work well. To address this issue, we describe recent advances in MCMC methods for these models and their implementation in the R package lgcp. Our suite of R functions provides an extensible framework for inferring covariate effects as well as the parameters of the latent field. We also present methods for Bayesian inference in two further classes of model based on the log-Gaussian Cox process. The first of these concerns the case where we wish to fit a point process model to data consisting of event-counts aggregated to a set of spatial regions: we demonstrate how this can be achieved using data-augmentation. The second concerns Bayesian inference for a class of marked-point processes specified via a multivariate log-Gaussian Cox process model. For both of these extensions, we give details of their implementation in R.
Highlights
A major goal of epidemiological research is to investigate the effects of environmental exposures on health outcomes
It is not necessary to specify an initial value for η or β as in the first line of code: by default, lgcp will initialise the Markov chain Monte Carlo (MCMC) using the prior mean for η, and for β it will initialise using the estimate obtained from an overdispersed Poisson glm fit of the cell counts against the covariates, and offset if appropriate
We have introduced four statistical models based around the log-Gaussian Cox process: a spatial point process model, an aggregated count model, a spatiotemporal point process model and a multivariate point process model
Summary
In the two sections we re-visit a point process dataset originally analysed in Prince, Chetwynd, Diggle, Jarner, Metcalf, and James (2001). Since we are using population as an explanatory variable, before we proceed to analyse the data we need to replace this covariate with the logarithm of population This is because under a Poisson model, we expect the number of cases to be proportional to the population at risk (and not the exponential of population). It is not necessary to specify an initial value for η or β as in the first line of code: by default, lgcp will initialise the MCMC using the prior mean for η, and for β it will initialise using the estimate obtained from an overdispersed Poisson glm fit of the cell counts against the covariates, and offset if appropriate.
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