\summary

Bivariate geostatistical models define random functions for two stochastic processes with known spatial locations. Existence of a Gaussian random fields can be assumed for each latent random variable. 
Ths Gaussianity assumption for the latent process is a convenient one for the inferences on the model
parameters and for spatial predictions once the joint distribution for a set of points is multivariate normal. The covariance matrix of this distribution should be positive-definite and to have the spatial variability structure between and among the attributes. Gelfand et al. (2004) and Diggle e Ribeiro Jr. (2007) suggested strategies for structuring this matrix, however there are few reports on comparing approaches. This work reports on a simulation study of bivariate models together with maximum likelihood estimators and spatial prediction under different sets of sampling locations space. 
Soil sample data from a field with 51.8 hectares is also analysed with the two soil attributes observed at 67 spatial locations. Data on pH and base saturation were submitted to spatial descriptive analysis, univariate and bivariate modeling and spatial prediction. 
To check for advantages of the adoption of univariate or bivariate models, 
the sample of the more expensive variable was divided into a modeling and testing subsamples. 
The first was used to fit geostatistical models, and the second was used to compare the spatial prediction precisions in the locations not used in the modeling process.

\vspace*{.5cm}
\noindent {\em Keywords}: Bivariate geostatistical Models; Gaussian random fields; Maximum likelihood estimators; Simulation study

%%% Local Variables:
%%% mode: latex
%%% TeX-master: "TESALQ"
%%% TeX-command-default: "PdfLaTeX"
%%% End:
