CODE | 52503 |
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ACADEMIC YEAR | 2022/2023 |
CREDITS |
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SCIENTIFIC DISCIPLINARY SECTOR | MAT/06 |
TEACHING LOCATION |
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SEMESTER | Annual |
PREREQUISITES |
Prerequisites
You can take the exam for this unit if you passed the following exam(s):
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TEACHING MATERIALS | AULAWEB |
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).
To formalise estimation problems (parametric and non-parametric) and statistical hypothesis testing in a rigorous mathematical framework, to formulate and apply appropriate regression models to various typologies of data sets.
At the end of the course students will be able to
Probability, Mathematical Analysis 1 and 2
Combination of traditionals lectures and exercises.
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.
Some academic years:
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.
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
Office hours: By appointment arranged by email <riccomagno@dima.unige.it>
EVA RICCOMAGNO (President)
SARA SOMMARIVA
FRANCESCO PORRO (President Substitute)
The class will start according to the academic calendar.
Written and oral exam.
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).
Date | Time | Location | Type | Notes |
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19/12/2022 | 09:00 | GENOVA | Compitino | |
19/12/2022 | 09:00 | GENOVA | Scritto | riservato agli studenti iscritti a.a.2021/2022 e anni accademici precedenti |
12/01/2023 | 09:00 | GENOVA | Scritto | riservato agli studenti iscritti a.a.2021/2022 e anni accademici precedenti |
12/01/2023 | 09:00 | GENOVA | Compitino | |
08/02/2023 | 09:00 | GENOVA | Scritto | riservato agli studenti iscritti a.a.2021/2022 e anni accademici precedenti |
08/02/2023 | 09:00 | GENOVA | Compitino | |
06/06/2023 | 09:00 | GENOVA | Scritto | |
06/07/2023 | 09:00 | GENOVA | Scritto | |
05/09/2023 | 09:00 | GENOVA | Scritto |
Students with DSA, disability or other special educational needs are recommended to contact the teacher at the beginning of the course, in order to organize teaching and assessment, taking in account both the class aims and the student's needs and providing suitable compensatory instruments.
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