CODE 52503 ACADEMIC YEAR 2024/2025 CREDITS 6 cfu anno 2 MATEMATICA 9011 (LM-40) - GENOVA 6 cfu anno 3 STATISTICA MATEM. E TRATTAM. INFORMATICO DEI DATI 8766 (L-35) - GENOVA 6 cfu anno 1 MATEMATICA 9011 (LM-40) - GENOVA SCIENTIFIC DISCIPLINARY SECTOR MAT/06 LANGUAGE Italian (English on demand) TEACHING LOCATION GENOVA SEMESTER 1° Semester PREREQUISITES Propedeuticità in ingresso Per sostenere l'esame di questo insegnamento è necessario aver sostenuto i seguenti esami: Mathematical Statistics and Data Management 8766 (coorte 2023/2024) PROBABILITY 87081 2023 Mathematical Statistics and Data Management 8766 (coorte 2024/2025) PROBABILITY 87081 2024 Mathematical Statistics and Data Management 8766 (coorte 2022/2023) PROBABILITY 87081 2022 TEACHING MATERIALS AULAWEB OVERVIEW An introduction to the classical theory of statistical models (model identification and estimation, parametric and not parametric models, exponential models), point estimation (moment method, likelihood method and invariant estimators) and methods of evaluating estimators (UMVUE estimators, Fisher information, Cramer-Rao inequality). AIMS AND CONTENT LEARNING OUTCOMES The course aims to frame the problems of parametric and non-parametric estimation and hypothesis testing in a rigorous context from a mathematical point of view and provide the theoretical basis for deepening the study of the large class of linear models. AIMS AND LEARNING OUTCOMES At the end of the course students will be able to recognise estimation problems (both parametric and non parametric) in applied contexts formulate them in a rigorous mathematical framework determine estimators of model parameters and evaluate their goodness write definitions, statements and demonstrations and produce related examples and counterexamples PREREQUISITES Probability, Mathematical Analysis 1 and 2 TEACHING METHODS Combination of traditionals lectures and exercises. SYLLABUS/CONTENT Review of essential probability including the notion of conditional probability and multivariate normal distribution. Statistical models and statistics|: the ideas of data sample and of statistical model, identifiability and regular models, the exponential family. Statistics and their distributions. Sufficient, minimal and sufficient, ancillary, complete statistics. The lemma of Neyman-Fisher. The Basu theorem. Point estimators and their properties: methods to find point estimators: moment methods, least square method, maximum likelihood method, invariant estimators. Methods to evaluate estimators: theorems of Rao-Blackwell and Lehmann-Scheffé. UMVU estimators. Expected Fisher information, Cramer-Rao inequality and efficient estimators. Statistical hypothesis testing: theorem of Neyman-Pearson for simple hypothesis, likelihood ration test. Introduction to Bayesian statistics: prior and posterior probability distributions, conjugate priors, improper and flat priors, comparison with the frequentist approach to estimation. At most one of the last two topics is part of the course for each given year. RECOMMENDED READING/BIBLIOGRAPHY Testi consigliati/Text books: G. Casella e R.L. Berger, Statistical inference, Wadsworth 62-2002-02 62-2002-09 D. A. Freedman, Statistical Models, Theory and Practice, Cambridge 62-2009-05 L. Pace e A. Salvan, Teoria della statistica, CEDAM 62-1996-01 M. Gasparini, Modelli probabilistici e statistici, CLUT 60-2006-08 D. Dacunha-Castelle e M. Duflo, Probabilites et Statistiques, Masson 60-1982-18/19/26 e 60-1983-22/23/24 A.C. Davison, Statistical Models, Cambridge University Press, Cambridge, 2003 Letture consigliate/Suggested reading: David J. Hand, A very short introduction to Statistics, Oxford 62-2008-05 L. Wasserman. All of Statistics, Springer J. Protter, Probability Essentials, Springer 60-2004-09 S.L. Lauritzen, Graphical models, Oxford University press 62-1996-14 D. Williams, Probability with Martingales, Cambridge Mathematical Textbooks, 1991 Appunti distribuiti a lezione/Handouts TEACHERS AND EXAM BOARD EVA RICCOMAGNO Ricevimento: For organizational issues contact by email Eva Riccomagno <riccomagno@dima.unige.it> Exam Board EVA RICCOMAGNO (President) SARA SOMMARIVA FRANCESCO PORRO (President Substitute) LESSONS LESSONS START The class will start according to the academic calendar. Class schedule The timetable for this course is available here: Portale EasyAcademy EXAMS EXAM DESCRIPTION Written and oral exam. ASSESSMENT METHODS In the written exam there are three or four exercises. Past exams with solutions are available on the websites. The oral exam consists of questions on both parts of the course. The course work done during the lab sessions might be subject of the oral exam (thus bring with you at the exams that course work). Exam schedule Data appello Orario Luogo Degree type Note 19/12/2024 09:00 GENOVA Scritto 09/01/2025 09:00 GENOVA Scritto 11/02/2025 09:00 GENOVA Scritto 05/06/2025 09:00 GENOVA Scritto 07/07/2025 09:00 GENOVA Scritto 05/09/2025 09:00 GENOVA Scritto FURTHER INFORMATION Students who have valid certification of physical or learning disabilities on file with the University and who wish to discuss possible accommodations or other circumstances regarding lectures, coursework and exams, should speak both with the instructor and with Professor Sergio Di Domizio (sergio.didomizio@unige.it), the Department’s disability liaison. Upon request by the students, the lectures and/or the exam can be held in English Prerequisite for the first part: Mathematical Analysis 1 and 2, Probability Agenda 2030 - Sustainable Development Goals No poverty Quality education Gender equality Decent work and economic growth