Ing Ind - Inf (Mag.)(ord. 270) - MI (475) ELECTRICAL ENGINEERING - INGEGNERIA ELETTRICA
055283 - BAYESIAN LEARNING AND MONTECARLO SIMULATION
The course aims to give an application-oriented introduction to the Bayesian statistical learning. Part of the course is devoted to a practical introduction to Monte Carlo techniques, that are fundamental tools in applied Bayesian statistics and in many other fields.
In Bayesian learning prior hypotheses/beliefs on probabilistic models are updated in the light of data, yielding to posterior beliefs. Bayes' Theorem describes this learning process in a coherent probabilistic language. In this framework, the course offers an operative view of Bayesian statistics, through examples and problems solved with the aid of R software. To this aim, a short introduction to R software and to some of its Bayesian packages is provided.
Risultati di apprendimento attesi
On successful completion of the course, students will be able to:
learn the appropriate terminology, understand the fundamental principles, tools and models of Bayesian Statistics (“Dublin Descriptors” DD 1, knowledge and understanding)
apply methods of statistical analysis to specific problems in electrical engineering; extract significant indicators from data; use statistical software (DD 2, applying knowledge and understanding)
operate and communicate the choices made, making independent judgements, when using Bayesian tools for dealing with statistical problems from the real world (DD 3)
the laboratory project will allow students to communicate clearly and convincingly the design choices made and work effectively as part of a team (DD 4, DD 5)
Principles of Bayesian learning. Quantifying uncertainty using probabilities. Likelihood, prior and posterior distributions: Bayes’Theorem for learning from data. Bayesian estimation and hypothesis testing. Posterior mean and variance, maximum a posteriori (MAP) estimate, posterior intervals, prediction, Bayes factor.
Basic models. Bayesian learning for proportions (Bernoulli model- Beta prior). Inference for mean and variance in normal model (Normal Gamma prior). Inference for count data (Poisson model Gamma prior). Generalizations: conjugate priors.
Statistical Computing. Introduction to R software for Bayesian analysis.
Monte Carlo Methods. Why sampling methods are needed: intractable integrals and sums. Monte Carlo integration.Importance sampling. Monte Carlo Markov Chain. Practical examples and implementation in R.
More complex models. A selection among these subjects: mixture of normal distributions and clustering (Expectation Maximization, Gibbs sampling), Bayesian linear regression models, classification (naive Bayes). Basics of Bayesian reliability models.
Applications to real data. Electrical load forecasting and electricity demand, Bayesian optimization for efficient uncertainty quantification in complex electrical/electronic systems.
Students will develop a short data analysis project (possibly in group), to enhance specific soft skills such as Making judgements, Communication skills and Ability in learning (DD 3,4,5).
Students are required to know some basic statistical notions (as, for example, the statistical topics in Metodi Analitici e Statistici per l’Ingegneria 091185) as well linear algebra and calculus.
Modalità di valutazione
The exam consists in the presentation of a statistical project. As a general rule, the projects will be developed in teams (2/3 persons) and discussed with the teacher during the course. Projects are focused on the statistical analysis of a dataset, using Bayesian tools and models. Data to analyze will be arranged together by the team and the instructor.
Each students’ team must hand over a project report (10-15 pages); the project illustration should be presented using slides on a laptop (about 20 minutes for each team).
After the exam:
the student will know the fundamental principles, tools and models of Bayesian Statistics [DD: 1]
he/she will be able to apply the acquired knowledge to statistical problems from the real world [DD: 2]
making independent judgements, the student will operate and communicate the choices made, when using Bayesian tools to solve statistical problems from the real world. [DD: 1,2,4]
Mary Kathryn Cowles, Applied Bayesian Statistics, Editore: Springer, Anno edizione: 2013
A. Gelman, J.B. Carlin, H.S. Stern, D. B. Dunson, A. Vehtari, D. B. Rubin, Bayesian Data Analysis, third ed, Editore: CRC Press, Anno edizione: 2013 Note:
Some more advanced topics
Tipo Forma Didattica
Ore di attività svolte in aula
Ore di studio autonome
Laboratorio Di Progetto
Informazioni in lingua inglese a supporto dell'internazionalizzazione
Insegnamento erogato in lingua
Disponibilità di materiale didattico/slides in lingua inglese
Disponibilità di libri di testo/bibliografia in lingua inglese
Possibilità di sostenere l'esame in lingua inglese
Disponibilità di supporto didattico in lingua inglese