Quick inference for log Gaussian Cox processes with non-stationary underlying random fields

摘要: Abstract For point patterns observed in natura, spatial heterogeneity is more the rule than exception. In numerous applications, this can be mathematically handled by flexible class of log Gaussian Cox processes (LGCPs); brief, a LGCP process driven an underlying random field (log GRF). This allows representation aggregation, vacuum and intermediate situations, with or less rapid transitions between these different states depending on properties GRF. Very often, covariance function GRF assumed to stationary. article, we give two examples where sizes (that is, number points) extents clusters are allowed vary space. To tackle such features, propose parametric semiparametric models non-stationary LGCPs non-stationarity included both mean Thus, contrast most other work inhomogeneous LGCPs, second-order intensity-reweighted stationarity not satisfied usual step procedure for parameter estimation based e.g. composite likelihood does easily apply. Instead fast three composite likelihood. We apply our modelling framework analyse datasets dealing fish aggregation reservoir dispersal biological particles.