corso|33502

The main objective of the course is to show the most popular techniques of non parametric inference, mainly from a Bayesian perspective. Covered topics include Dirichlet processes and its ramifications with special emphasis to applications of above methods in data science applications. General objectives: The aim of the course is to provide the basis of the theory of sequences and series of functions and of the theory of functions of complex variable, with applications to Laplace transform and easy applications to the Fourier transformation. Specific objectives: To know the basis of the theory of approximation, with particular attention to the notions of pointwise and uniform convergence for sequences of functions (of one or more real variables) and of pointwise, absolute, uniform and total convergence for series of functions, in particular for power series and trigonometric series. Standard deviation and convergence in quadratic mean, Parseval equality for trigonometric series. To know the basis of the theory of functions of complex variable, with particular attention to the notions of holomorphy, of singular point, of residue, of Laplace transform and inversion formula. Knowledge and understanding: Being able to analyse the behaviour of sequences of functions (of one or more real variables or of one complex variable) and of series of functions of real or complex variable from the point of view of the various notions of convergences. Being able to reconstruct a signal starting from its Laplace transform, to solve Cauchy problems for linear differential equations with constant coefficients by Laplace transform and to calculate simple Fourier transforms. Apply knowledge and understanding: Being able to analyse the behaviour of sequences of functions (of one or more real variables or of one complex variable) and of series of functions of real or complex variable from the point of view of the various notions of convergences. Being able to reconstruct a signal starting from its Laplace transform, to solve Cauchy problems for linear differential equations with constant coefficients by Laplace transform and to calculate simple Fourier transforms.