A comparative study of two approaches to modelling and prediction in spatial statistics

Methods based on regionalized variables theory, commonly known as geostatistics, have been widely used since more than three decades to predict/estimate spatial distributed data, namely mineral resources, with quite good results. However, some restrictive theoretical assumptions, such as the need of some kind of stationarity of data and the linearity of the predictor/estimator, are often wrong options in many applications. An alternative approach based on a finite mixture modelling, or cluster weighted modelling (CWM) technique, is presented and compared, in its theoretical and practical aspects, with the geostatistical methodology. CWM is a general non-linear framework based on the estimation of joint density functions allowing the calculation of the conditional probability function of the target values given their locations. Validation tests are performed in a 2D case study, where testing data proceeds from a soil contaminated by a heavy metal. The results of ordinary kriging and CWM estimations show a very good agreement with actual data. Keywords: Non-linear regression, Geostatistics, Ordinary kriging, Finite mixture modelling, Cluster weighted modelling.