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. 

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)

SYLLABUS/CONTENT

Estimation. Populations, samples, sources of uncertainty and point estimators. Properties of point estimators. 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.

RECOMMENDED READING/BIBLIOGRAPHY

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)

GABRIELE MOSAICO

SARA SOMMARIVA (President Substitute)

GIACOMO LANCIA (Substitute)

LESSONS

LESSONS START

According to the academic calendar

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.

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

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.