1) Types of variability. Assessment of variability. Jenny’s and Scorpan models;
2) Traditional cartographic approach. Delineation in homogeneous areas. Principles on which the traditional approach is based;
3) Traditional statistical model of spatial variability. Assumptions of normality and independence of errors;
4) Calculation of basic statistics. Fitting of a mathematical model;
5) Pros and cons of the traditional approach. Need for an alternative approach. Illustration of a case study;
6) Classification of the causes of variation. Comparison between traditional and modern approach;
7) Recalls of the traditional approach and its limitations compared to the stochastic approach;
8) Improvement of the new approach compared to the traditional one. New model of spatial prediction. Basic principles of the theory of regionalized variables;
9) Definition of stochastic variables. Definitions and formalism related to stochastic variables. Concepts of first and second order stationarity and intrinsic stationarity;
10) Definition and calculation of the experimental variogram. Omnidirectional and directional variograms. Characteristic parameters of the theoretical variogram;
11) Fitting of an authorized mathematical model to the experimental variogram. Various types of authorized models and their characteristics;
12) Definition of anisotropy. Geometric and zonal anisotropy. Mathematical treatment of different types of anisotropy;
13) Need for an estimate of the error. Definition of simple and Ordinary Point Kriging. Derivation of the Kriging system. Calculation of the variance of Kriging estimation;
14) Properties of Point Kriging. Display of Kriging weights and definition of interpolation neighbourhood. Limitations of Point Kriging;
15) Definition of Block Kriging. Concept of Support. Derivation of Block Kriging system. Calculation of the mean variogram (regularization). Differences between Point and Block Kriging;
16) Definition of Polygon Kriging. Statistical comparison between polygons. Suggestions on the choice of support. Cross Validation. Hybrid methods. Local Kriging.
17) Non-stationary Geostatistics. Over-estimation error (Alpha). Under-estimation error (Beta)