Part I Probability --------------------- Outcomes, Events & Probability. Conditional Probability & Independence. Bayes' Theorem: Interpretation & Use. Random Variables and Random Vectors. Directed Graphical Models. Expected Value, Variance and Covariance. Univariate and Multivariate Distributions. Generating Functions and Convergence Theorems. Part II Statistics --------------------- The Empirical Distribution and the Bootstrap Statistical Modelling: the Likelihood Function. Parameter Estimation: Point and Interval Estimation. Hypothesis Testing. Alternative Inferential Frameworks: Frequentist vs Bayesian Inference.

Riferimenti principali: F.M. Dekking, C. Kraaikamp, H.P. Lopuhaa, L.E. Meester (2007). A Modern Introduction to Probability and Statistics. Springer. L. Wasserman (2004). All of Statistics: A Concise Course in Statistical Inference. Springer.

Teaching material will be also delivered through the Sapienza elearning platform Moodle at the following address: https://elearning2.uniroma1.it/course/view.php?id=4951 Course Material and Main Reference Books • Course lecture notes (slide available at the https://elearning2.uniroma1.it/course/view.php?id=7253) • R or R+Jags commented codes • Peter Hoff, A First Course in Bayesian Statistical Methods. Springer-Verlag Inc, 2009. • Jean-Michel Marin and Christian P. Robert, Bayesian Core: A Practical Approach to Computational Bayesian Statistics, Springer, 2007 • Christian P. Robert and George Casella. Monte Carlo statistical methods (2nd ed.. Springer-Verlag Inc, 2004. • Ioannis Ntzoufras, Bayesian Modeling Using WinBUGS. Wiley, 2009. • Peter Congdon. Bayesian Statistical Modelling (2nd ed.). Wiley, 2006