OVERVIEW

Introduction to Statistical Inference

AIMS AND CONTENT

LEARNING OUTCOMES

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

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. 

The computer laboratory sessions are mandatory for SMID students. Their aim is to practice the application of the theoretical models learnt during classroom lectures on simple real case studies and data sets. During the lab sessions the student will be able to verify his/her level on understanding of the theory and its application.

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

Lectures and exercises in the classroom, computer lab with the help of R software (optional for students of the bachelor's and master’s degrees in mathematics). Attendance at the labs is mandatory for SMID students for at least 75%.

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 and examples of inference by simulation and resampling. 

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

LESSONS

LESSONS START

According to the academic calendar

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The exam consists of a written and an oral part.

Three closed book written examinations lasting 55 minutes each are given during the year. Each one consists of two or three exercises to be completed with the sole aid of a calculator and tables and is valued at a maximum of ten points. Passing all three assignments, with a grade greater than or equal to six each, exempts you from the written exam in the June, July and September sessions.

For students who have not completed the three assignments or have not passed them or refuse their total grade or take the exam in the winter session, the written exam consists of two parts to be completed on the same day. A first, more theoretical test, lasting three quarters of an hour, without notes or textbooks, with a maximum score of eight points. A second written test (lasting two hours, in which it is possible to keep notes and textbooks) consists of more calculative exercises and is valued at a maximum of 23 points. To be admitted to the oral exam, you must have at least 16 total points from the two written tests.

The grade obtained in the written exam replaces that of the assignments (those who submit them lose the assignments). The written tests are valid only for the session in which they are taken.

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For students with disabilities or with DSA, please refer to the Other Information section.

ASSESSMENT METHODS

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

An exercise of the on-course examination and the two-hour open-book examination evaluates the acquired ability to apply the theoretical ideas for simple data analysis.

FURTHER INFORMATION

Students who have valid certification of physical or learning disabilities on file with the University and who wish to discuss possible accommodations or other circumstances regarding lectures, coursework and exams, should speak both with the instructor and with Professor Sergio Di Domizio (sergio.didomizio@unige.it), the Department’s disability liaison.

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