CODE 48384 2023/2024 6 cfu anno 2 MATEMATICA 9011 (LM-40) - GENOVA 6 cfu anno 1 MATEMATICA 9011 (LM-40) - GENOVA 8 cfu anno 2 STATISTICA MATEM. E TRATTAM. INFORMATICO DEI DATI 8766 (L-35) - GENOVA 8 cfu anno 3 MATEMATICA 8760 (L-35) - GENOVA 6 cfu anno 3 MATEMATICA 8760 (L-35) - GENOVA SECS-S/01 GENOVA 2° Semester AULAWEB

## OVERVIEW

Introduction to Statistical Inference

## AIMS AND CONTENT

### LEARNING OUTCOMES

a) To provide an introduction to concepts and techniques from statistical inference which are fundamental to provide a probabilistic measure of the error committed when estimation is based on a sample from a large population. b) To deal with theoretical and practical elements of the design, analysis and inference of survey data obtained by probabilistic sampling.

### AIMS AND LEARNING OUTCOMES

At the end of the course students will be able:

• to explain the key points defining exploratory data analysis versus statistical inference based on finite samples
• to possess the main concepts and techniques for computing point estimates, confidence intervals and performing hypothesis testing and for evaluating them
• to identify the suitable statistical technique and perform the analysis of simple data sets.

By participating to the work groups, debating solution strategies and their presentation, comparing the learning strategies of the different members of the group also with the feedback from the individual mock exams, at the end of the course the student will have acquired the following skills at a basic level at a basic level

• alphabetical-functional
• personal competence
• ability to learn to learn
• social competence

### PREREQUISITES

Mathematical Analysis: function of a variable, integral calculus.
Algebra: elements of vector and matrix algebra.
Probability: elementary probability

### TEACHING METHODS

Combination of traditional lectures (40 hours) and exercises sessions (24 hours)

Four guided group exercises to develop basic literacy skills, personal competence, ability to learn to learn, social competence.

### SYLLABUS/CONTENT

Estimation. Populations, samples, sources of uncertainty and point estimators. Properties of point estimators. Delta method. Some point estimators and their probability distributions. Confidence intervals.
Hypothesis tests. How to define and use a statistical test (hypotheses, errors of the first and second type, critical region). Parametric tests. Tests of large samples. Comparative tests. Some non-parametric tests.
Statistics and tests for linear multiple models. Confidence intervals for the parameters, estimated values and residuals, "studentized" residuals, test of hypotheses on single coefficients and on subsets of coefficients. Forecast.

1. Casella G., Berger R.L. (2002), Statistical Inference, Pacific Grove, CA: Duxbury

2. Mood A.M., Graybill F.A., Boes D.C. (1991), Introduction to the Theory of Statistics, McGraw-Hill, Inc.

3. Ross S.M. (2003), Probabilità e statistica per l’ingegneria e le scienze, Apogeo, Milano

4. Wasserman L. (2005), All of Statistics, Springer

## TEACHERS AND EXAM BOARD

### Exam Board

EVA RICCOMAGNO (President)

GIACOMO LANCIA

GABRIELE MOSAICO (President Substitute)

SARA SOMMARIVA (President Substitute)

## LESSONS

### Class schedule

The timetable for this course is available here: Portale EasyAcademy

## EXAMS

### EXAM DESCRIPTION

The exam consists of a written and a oral part.

During the semester there will be three (not evaluated) mock exams. The lecture after each mock exam will start with a 15-minute closed-book written examination.

The first two closed-book examinations are evaluated at most 3 marks and the third one at most 2 marks, for a maximum total of 8 marks.

For the students who attempted all of the three closed-book examinations, the final written examination consists of a 2-hour open book examination, which is evaluated at most 23 marks to be added to the marks of the three on-course closed-book examinations.

For the students who did not attempt the three closed-book examinations, the final written examination consists of two parts: a 45-minute closed-book examination and a 2-hour open-book examination. The closed-book part is evaluated at most 8 points, the open-book part is evaluated at most 23 points.

To be admitted to the oral examination, are required either a total of 5 points from the intermediate exams or a total of 16 points from the two parts of the written exam.

The mark obtained from the intermediate exams are valid until February. The mark from the written parts is valid only once.

### ASSESSMENT METHODS

The on-course examination and the closed-book part of the final examination test the comprehension of the theory.

The two-hour open-book examination evaluates the acquired ability to apply the theoretical ideas for simple data analysis.

### Exam schedule

Data appello Orario Luogo Degree type Note
22/01/2024 09:00 GENOVA Scritto
15/02/2024 09:00 GENOVA Scritto
17/06/2024 09:00 GENOVA Scritto
22/07/2024 09:00 GENOVA Scritto
13/09/2024 09:00 GENOVA Scritto

### 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.

Upon request by the students, the lectures and/or the exam can be held in English.