CODE  52503 

ACADEMIC YEAR  2021/2022 
CREDITS 

SCIENTIFIC DISCIPLINARY SECTOR  MAT/06 
TEACHING LOCATION 

SEMESTER  1° Semester 
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).
The second part develops the main aspects of the theory and practice of the analysis of time series in the timedomain and hints to the analysis in the frequency domain.
To formalise estimation problems (parametric and nonparametric) and statistical hypothesis testing in a rigorous mathematical framework. To intruduce the analysis of time series, combining practical and theorical considerations.
At the end of the course students will be able to
At the end of the course students will
Combination of traditionals lectures and, only for the second part, lab sessions with the software R.
Program of the first part of the course:
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.
Program of the second part of the course:
Time series: exploratory analysis. The notions of stationarity and ergodicity. Strong and weak stationary processes. Autocovariance function and partial autocovariance function. SARIMA models.
Prima Parte/First part:
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
Second Part:
C. Chatfield (1980). The analysis of Time Series: an introduction, Chapman and Hall
Rob J Hyndman and George Athanasopoulos, Forecasting: Principles and Practice, Monash University, Australia https://otexts.com/fpp2/
R.D. Pend , F. Dominici, Statistical methods for environmental epidemiology with R. A case study in air pollution and Health
R.H. Shumway, D.S. Stoffe, Time series analysis and its applications with examples in R
Office hours: By appointment arranged by email with Luca Oneto luca.oneto@unige.it and Fabrizio Malfanti <fabrizio.malfanti@intelligrate.it> For organizational issues contact by email Eva Riccomagno <riccomagno@dima.unige.it>
EVA RICCOMAGNO (President)
MARIA PIERA ROGANTIN (President Substitute)
The class will start according to the academic calendar.
The two parts of the course are examined together. Written and oral exam. For the second part written exam with multiple choice and open questions. Two group projects on topics agreed with the teachers. Discussion of the reports and written test.
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).
Main points of evaluation are the level of acquisition of the learning objectives and the ability to communicate in a written report the data analyzes carried out during the course.
Pagina web dell'insegnamento:
Prima parte: http://www.dima.unige.it/~riccomag/Teaching/StatisticaMatematica.html
Seconda parte: http://www.dima.unige.it/~rogantin/ModStat/
Prerequisiti Prima Parte: Analisi Matematica I e 2. Calcolo delle Probabilità .
Prerequisiti Seconda Parte: Argomenti di Statistica inferenziale e della prima parte di Statistica Matematica (quest'ultima svolta in parallelo) con corrispondenti prerequisiti.
Web pages of the couse are
for the first part: http://www.dima.unige.it/~riccomag/Teaching/StatisticaMatematica.html
for the second part: http://www.dima.unige.it/~rogantin/ModStat/
Prerequisite for the first part: Mathematical Analysis 1 and 2, Probability
Prerequisite for the second part: Statistical inference and in parallel the first part of Mathematical Statistics.