Probability and conditional probability; stochastic processes (Markov chains); statistical inference; Bayesian inference

Graphical representation of conditional independence; Learning when to use and how to fit both discrete and Gaussian graphical models; fitting and interpreting log linear models; hidden Markov models; estimation and interpretation of hidden Markov models; use of statistical software for model fitting.

1) Basic concepts of graphical models a) Directed and non-directed graphs. b) Conditional independence and its graphical representation c) Representing graphical models in R d) The naive Bayes classifier as a graphical model 2) Log-linear models a) Representation as graphical models b) Fitting log-linear models c) Practical example 3) Bayesian networks a) Representation b) Classical and Bayesian approaches c) How to infer causality d) Practical example 4) Gaussian networks and mixed networks a) Representation and adjustment b) Practical example 5) More complex graphical models a) Algorithms b) Examples 6) Hidden Markov models a) Structure. b) Algorithms for estimation. c) Interpretation of hidden states. d) Practical examples. e) Quick fitting of hidden Markov models: filters.

Theoretical and computer practical classes with presentation and resolution of real problems, individual and group work.