Introduction to the basics of mathematical statistics and data analysis, including quantitative numerical experiments using suitable statistical software.
Curriculum
teacher profile teaching materials
Point estimators: method of moments, maximum likelihood estimators and Bayes estimators. EM algorithm.
How to evaluate estimators: bias, consistency and mean square error. UMVU estimators and efficient estimators.
Confidence interval: the concept of pivotals, asymptotic methods and the delta method.
Hypothesis testing: definitions, likelihood ratio test and duality with confidence interval. Uniformly most powerful tests.
Non-parametric methods: Goodness-of-fit test for discrete and continuum variables, contingency tables and Kolmogorov-Smirnov test.
Other topics: analysis of variance (ANOVA), linear regression, generalized linear regression and logistic regression.
Casella e Berger
Duxbury
2nd edition.
Programme
Introduction to statistics: random sampling of finite and infinite populations. Definition of the statistical model and the concept of statistics. Example of statistics. Properties of statistics: sufficient, minimal and complete statistics.Point estimators: method of moments, maximum likelihood estimators and Bayes estimators. EM algorithm.
How to evaluate estimators: bias, consistency and mean square error. UMVU estimators and efficient estimators.
Confidence interval: the concept of pivotals, asymptotic methods and the delta method.
Hypothesis testing: definitions, likelihood ratio test and duality with confidence interval. Uniformly most powerful tests.
Non-parametric methods: Goodness-of-fit test for discrete and continuum variables, contingency tables and Kolmogorov-Smirnov test.
Other topics: analysis of variance (ANOVA), linear regression, generalized linear regression and logistic regression.
Core Documentation
Statistical InferenceCasella e Berger
Duxbury
2nd edition.
Reference Bibliography
Probabilità e statistica per l'ingegneria e le scienze Ross Apogeo Education Terza edizione Laboratorio di Statistica con R Ieva, Masci e Paganoni PearsonType of delivery of the course
Lectures with exercises during the lectures and a project for the analysis of real data (in groups of 2 or 3 students).Attendance
Attendance of lectures is recommended.Type of evaluation
Final written exam with questions of conceptual and numerical nature. Homeworks. A project for the analysis of real data (in groups of 2 or 3 students), to apply the methods studied during the lectures.Mutuazione: 20410440 ST410-INTRODUZIONE ALLA STATISTICA in Scienze Computazionali LM-40 (docente da definire)