Fundamentals of Statistical Learning I

Obiettivi formativi

Goals Statistical Methods in Data Science is a two-semester course aimed at providing the fundamental tools for: setting up probabilistic models; understanding the basic principles of the main inferential problems: estimation, hypothesis testing, model checking and forecasting; understanding and contrasting the two main inferential paradigms, namely frequentist and Bayesian statistics; implementing inference on observed data through both optimization and simulation-based (approximation) techniques such as: Bootstrap, Monte Carlo and Monte Carlo Markov Chain (MCMC) Understanding comparative merits of alternative strategies developing statistical computations within a suitable software environment like R (www.r-project.org), OpenBUGS (http://openbugs.net/w/FrontPage) and STAN (http://mc-stan.org/). Knowledge and understanding On successful completion of this course, students will: know the main statistical principles, inferential problems, paradigms and algorithms; assess the empirical and theoretical performance of different modeling approaches; know the main platforms, programming languages to develop effective implementations. Applying knowledge and understanding Besides the understanding of theoretical aspects, thanks to applied homeworks and a dedicated laboratory in the second semester focused on Bayesian modeling, students will be constantly challenged to use and evaluate all the techniques they have learned as well as to propose new modelization suitable for specific tasks at hand. Making judgements On successful completion of this course, students will develop a positive critical attitude towards the empirical and theoretical evaluation of statistical methodologies and results. Communication skills In preparing the report and oral presentation for the final project of the second semester laboratory, students will learn how to effectively communicate information, ideas, problems and solutions to specialists but also to a general audience. Capacità di apprendimento | Learning Skill In this course students will develop the skills necessary for a successful understanding and application of new statistical methodologies together with their effective implementation. The goal is of course to grow an active attitude towards continued learning throughout a professional career.

Canale 1
PIERPAOLO BRUTTI Scheda docente

Programmi - Frequenza - Esami

Programma
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.
Prerequisiti
Probabilità di Base, Algebra Lineare, Analisi Matematica
Testi di riferimento
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.
Modalità insegnamento
Lezioni Frontali
Frequenza
Facoltativa
Modalità di esame
Homeworks (35%) + Written Exam + Oral Check (65%)
Bibliografia
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.
Modalità di erogazione
Lezioni frontali e attività laboratoriali
  • Anno accademico2025/2026
  • CorsoData Science
  • CurriculumCurriculum unico
  • Anno1º anno
  • Semestre1º semestre
  • SSDSECS-S/01
  • CFU9