An Overview of Approaches to the Analysis and Modelling of Multivariate Geostatistical Data

We give an overview of existing approaches for the analysis of geostatistical multivariate data, namely spatially indexed multivariate data where the indexing is continuous across space. These approaches are divided into two classes: factor models and spatial random field models. Factor models may be further subdivided into a descriptive sub-class, where the factors are directly obtainable as linear combinations of the manifest variables, and an inferential subclass, where the factors are latent quantities that have to be estimated from the data. Spatial random field models include a variety of different types, the most prominent being the proportional correlation model, the linear coregionalisation model, and several convolution-based models. We provide an overview of the different approaches, and draw out some connections between them.