Lectures proposed (Mod. A)
An introduction to stochastic modeling: from random variables and random vectors to random processes and fields.
Review of basics: Random variables and random vectors. Mean and covariance propagation laws. Sample variables. Estimators. Tests. Observation error modeling and error covariance propagation within the least squares interpolation problem. Geometric interpretation of the least squares solution and the orthogonalization of the normal matrix. Outlier detection.
Practice and laboratory sessions proposed (Mod. A)
Practice lessons with numerical examples will be given and exercises will be proposed to make students more familiar with the proposed techniques. Laboratory sessions will be devoted to the implementation of the following algorithm:
 Exact and least squares polynomial interpolation. Test on least squares nested models. Test on least squares parameters.
Lectures proposed (Mod. B)
Data gridding: nearest neighbor, distance weighted interpolation. Commission and omission error in data interpolation and error evaluation with the leave one out technique.
Data classification: hierarchical and optimization techniques. Stochastic techniques. Clasification quality evaluation.
Discrete Fourier Transform.
The stochastic modeling of deterministic interpolation residuals. The concepts of stationary signals and homogeneous and isotropic random fields, empirical variogram and covariance function estimation and the linear prediction with kriging techniques.
Practice and laboratory sessions proposed (Mod. B)
Practice lessons with numerical examples will be given and exercises will be proposed to make students more familiar with the proposed techniques. Laboratory sessions will be devoted to the implementation of the following algorithm:
 Hierarchical Classification: divisive and agglomerative clustering algorithm implementation. Partitioning around medoids by minimization of a target function. Maximum likelihood classification.
 DFT
 Stochastic prediction: empirical covariance/variogram function estimation and modeling. Simple kriging and collocation.
 GramSchmidt orthogonalization. Cholesky decompostition.
 Least squares interpolation with linear and cubic splines. Tichonov regularization.
