CODE  52503 

ACADEMIC YEAR  2022/2023 
CREDITS 

SCIENTIFIC DISCIPLINARY SECTOR  MAT/06 
TEACHING LOCATION 

SEMESTER  Annual 
PREREQUISITES 
Prerequisites
You can take the exam for this unit if you passed the following exam(s):

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, CramerRao inequality).
To formalise estimation problems (parametric and nonparametric) 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 NeymanFisher. 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 RaoBlackwell and LehmannScheffé. UMVU estimators. Expected Fisher information, CramerRao inequality and efficient estimators.
Some academic years:
Statistical hypothesis testing: theorem of NeymanPearson 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 62200202 62200209
D. A. Freedman, Statistical Models, Theory and Practice, Cambridge 62200905
L. Pace e A. Salvan, Teoria della statistica, CEDAM 62199601
M. Gasparini, Modelli probabilistici e statistici, CLUT 60200608
D. DacunhaCastelle e M. Duflo, Probabilites et Statistiques, Masson 60198218/19/26 e 60198322/23/24
A.C. Davison, Statistical Models, Cambridge University Press, Cambridge, 2003
Letture consigliate/Suggested reading:
David J. Hand, A very short introduction to Statistics, Oxford 62200805
L. Wasserman. All of Statistics, Springer
J. Protter, Probability Essentials, Springer 60200409
S.L. Lauritzen, Graphical models, Oxford University press 62199614
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 

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 
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