Gaussian random field models for spatial data

Spatial data contain information about both the attribute of interest as well as its location. Examples can be found in a large number of disciplines including ecology, geology, epidemiology, geography, image analysis, meteorology, forestry, and geosciences. The location may be a set of coordinates, such as the latitude and longitude associated with an observed pollutant level, or it may be a small region such as a county associated with an observed disease rate. Following Cressie (1993), we categorize spatial data into three distinct types: (i) geostatistical or point-level data, as in the pollutant levels observed at several monitors across a region, (ii) lattice or ‘areal’ (regionally aggregated) data, for example U.S. disease rates provided by county, and (iii) point process data, where the locations themselves are random variables and of interest, as in the set of locations where a rare animal species was observed. Point processes where random variables associated with the random locations are also of interest