CODE 108582 2024/2025 MAT/06 Italian (English on demand) GENOVA 2° Semester AULAWEB

## OVERVIEW

Two important areas of Statistics are introduced: sampling theory and time series analysis. The first part deals with theoretical and practical elements of the design, analysis and inference of survey data obtained by probabilistic sampling. The second part develops the main aspects of the theory and practice of the analysis of time series in the time-domain and hints to the analysis in the frequency domain.

## AIMS AND CONTENT

### LEARNING OUTCOMES

The course introduces the student to the exploratory statistical analysis of multivariate data by pointing out the mathematical aspects and by developing the essential skills for the interpretation of the data under investigation. Laboratory sessions provide students with the opportunity to analyse, discuss, and solve real problems.

### AIMS AND LEARNING OUTCOMES

At the end of the course students will be able to

• judge the validity of a sample survey
• plan and analyze simple sample surveys also by aid of software
• evaluate mathematical properties of a probabilistic sample
• develop further knowledge about the theory and practice of statistical sampling
• present a report with the analysis of a sample and a critique of its design

At the end of the course students will

• be able to perform the analysis of simple time series in the time domain also with software
• be able to develop further theoretical and computational knowledge for statistical analysis of time series
• be able to present a simple report about the statistical analysis of a time series
• possess the essential mathematical and statistical knowledge related to time series

By participating in the planned group activities, at the end of the course the student will have acquired the following basic skills

• alphabetical-functional (group writing up and individual precentation of group work)
• proficiency in project creation (choice of the project, data sets and statistical/mathematical techniques, choice of both written and oral presentation styles)
• ability to learn to learn (group learing of topics essential for the analysis)
• social competence, advanced level (subsumed by the amount and types of choices to be made by the group)

### PREREQUISITES

Combination of traditionals lectures and lab sessions with the software R.

### TEACHING METHODS

Combination of traditional lectures and lab sessions with the software R.

Group activities to develop basic literacy skills, project creation skills, ability to learn to learn and advanced social skills.

### SYLLABUS/CONTENT

Statistical sampling from a finite population. Simple random sampling with and without replacement. Stratified sampling. Proportional allocation and optimal allocation. Statistical estimators of means and their variances.

Time series: exploratory analysis. The notions of stationarity and ergodicity. Strong and weak stationary processes. Autocovariance function and partial autocovariance function. SARIMA models.

Sampling theory
1. Vic Barnett Sample Survey, Principle and methods, Third Edition, John Wiley & Sons, Ltd, 2002
2. William Cochran, Sampling Techniques, John Wiley & Sons, 1977
3. Sharon L. Lohr, Sampling: Design and Analysis. Second Edition, Brooks/Cole, 2010
4. Formulario ed alcuni esercizi su aulaweb (al sito del corso, in file) oppure http://www.dima.unige.it/ rogantin/StatInd/index.htm

Time series
1.C. Chatfield (1980). The analysis of Time Series: an introduction, Chapman and Hall
2. Rob J Hyndman and George Athanasopoulos (2nd edition). Forecasting: Principles and Practice, Monash University, Australia https://otexts.com/fpp2/
3. R.D. Pend e F. Dominici (2008). Statistical methods for environmental epidemiology with R. A case study in air pollution and Health, Wiley
4. R.H. Shumway e D.S. Stoer (2000). Time series analysis and its applications with examples in R, Springer

## LESSONS

### Class schedule

The timetable for this course is available here: Portale EasyAcademy

## EXAMS

### EXAM DESCRIPTION

Written exam with multiple choice and open questions. Two group projects on topics agreed with the teachers. Discussion of the reports and written test.

### ASSESSMENT METHODS

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.

### FURTHER INFORMATION

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.