Mathematics

ALESSANDRA FAGGIONATO
ALESSANDRA FAGGIONATO

General objectives: Introduce the student to the fundamental results of mathematical statistics and to the most significant applications, also through the discussion of concrete cases and statistical software.
 
Specific objectives:
 
Knowledge and understanding: at the end of the course the student will have acquired the basic notions and results concerning the problems of punctual estimation, by interval and the problems of hypothesis testing, as well as the main methods with which they are faced: method of moments, of the maximum likelihood and generalizations.
 
Apply knowledge and understanding: at the end of the course the student will be able to assess the degree of accuracy with which, in simple statistical problems, parameters can be estimated or validated on these, implementing these responses in an appropriate software.
 
Critical and judgmental skills: the student will be able to appreciate the probabilistic tools useful for dealing with statistical problems and the various approaches to resolving them.
 
Communication skills: ability to expose the contents in the oral part of the assessment and in any theoretical questions present in the written test.
 
Learning skills: the acquired knowledge will allow a subsequent study of more recent and advanced aspects of mathematical statistics.

General objectives: Introduce the student to the fundamental results of mathematical statistics and to the most significant applications, also through the discussion of concrete cases and statistical software.

Specific objectives:

Knowledge and understanding: at the end of the course the student will have acquired the basic notions and results concerning the problems of punctual estimation, by interval and the problems of hypothesis testing, as well as the main methods with which they are faced: method of moments, of the maximum likelihood and generalizations.

Apply knowledge and understanding: at the end of the course the student will be able to assess the degree of accuracy with which, in simple statistical problems, parameters can be estimated or validated on these, implementing these responses in an appropriate software.

Critical and judgmental skills: the student will be able to appreciate the probabilistic tools useful for dealing with statistical problems and the various approaches to resolving them.

Communication skills: ability to expose the contents in the oral part of the assessment and in any theoretical questions present in the written test.

Learning skills: the acquired knowledge will allow a subsequent study of more recent and advanced aspects of mathematical statistics.

Basic course in Probability

Introduction to statistics
- Parametric and non-parametric statistical models
- Principles of data reduction: sufficient statistics

Point estimate and confidence intervals
- methods of research of estimators
- optimality criteria
- maximum likelihood estimators
- Bayesian estimators
- confidence intervals
- asymptotic properties

Hypothesis test
- case of simple hypotheses
- composite hypotheses
- optimality criteria
- asymptotic properties

Linear regression
- least squares method
- the normal case

Some non-parametric models.

The program may be changed on request of the public.

Teacher's notes
Wasserman, All of Statistics: A Concise Course in Statistical Inference
H.-O. Georgii, Stochastics Introduction to Probability and Statistics
G. Casella, R. Berger: Statistical Inference

On site lessons about theory and exercises

Although not mandatory, it is strongly recommended to follow the course in presence

Written and oral exam

See the Teacher's webpage for previous written exams

• x
  • Books: u