ABSTRACT
Geostatistical data provide information of a spatially continuous phenomenon that has been measured at particular sites. This type of data may represent, for example, air pollution levels taken at a set of monitoring stations or disease prevalence survey data at a collection of sites. A Gaussian random field (GRF) is a collection of random variables where observations occur in a continuous domain, and where every finite collection of random variables has a multivariate normal distribution. This chapter shows how to generate realizations of several Gaussian random fields using the geoR package. Other packages that can be used to simulate Gaussian random fields include RandomFields. Beyond a certain separation distance known as the range, the semivariogram levels off and reaches a nearly constant value referred to as the sill. This indicates that spatial dependence between observations decays with distance within the range, and beyond that range, observations become spatially uncorrelated, resulting in a near constant variance.
