Bivariate or multivariate statistics: two-dimensional distributions, conditional averages, covariance and correlation, random variables as vectors, Hilbert space of random variables.
INTRODUCTION TO RANDOM FIELD THEORY: joint distribution of many random variables, the vector space of random variables, Covariance function and Positively Defined Functions, covariance models, simplified Random Fields.
STRUCTUAL ANALYSIS: Analysis of the concept of spatial correlation, definition of the barogram and its physical meaning, calculation and interpretation of the barogram, models of barograms, the barogram as a generalized covariance.
Spatio-temporal mapping: the projection algorithm and its geometric interpretation, simple and regular kriging, cases of algorithm failure and their treatment, trend treatment, uncertain data, spatio-temporal interpolation, error estimation.
APPLICATIONS IN MINING: Density optimization of exploratory drilling canvass density, mineral reserve estimation, estimation error maps.
APPLICATIONS IN HYDROGEOLOGY - GEOMETRY: Combined use of causal and stochastic models for the interpolation of hydrogeological measurements, spatial correlation of geochemical parameters.
APPLICATIONS IN GEOTHERMOLOGY: Combined use of causal and stochastic models for the description of geothermal reservoirs
APPLICATIONS IN SOIL - ROCK ENGINEERING: Spatial distribution of soil - rock mass parameters, correlation of parameters, combined use of causal and stochastic models.
APPLICATIONS TO ENVIRONMENTAL POLLUTION EVALUATION: Spatio-temporal pollution mapping, correlation of pollutant distributions.
APPLICATIONS TO EPIDEMIOLOGY: Combined use of causal and stochastic epidemiological models to visualise the spread of public health and safety parameters.
