The role of simulation in modelling spatially correlated data

Three approaches to modelling spatial data in which simulation plays a vital role are described and illustrated with examples. The first approach uses flexible regression models, such as generalized additive models, together with locational covariates to fit a surface to spatial data. We show how the bootstrap can be used to quantify the effects of model selection uncertainty and to avoid oversmoothing. The second approach, which is appropriate for binary data, allows for local spatial correlation by the inclusion in a logistic regression model of a covariate derived from neighbouring values of the response variable. The resulting autologistic model can be fitted to survey data obtained from a random sample of sites by incorporating the Gibbs sampler into the modelling procedure. We show this modelling strategy can be used not only to fit the autologistic model to sites included in the survey, but also to estimate the probability that a certain species is present in the unsurveyed sites. Our third approach relates to the analysis of spatio-temporal data. Here we model the distribution of a plant of animal species as a function of the distribution at an earlier time point. The bootstrap is used to estimate parameters and quantify their precision.