Degree course: 
Corso di Second cycle degree in MATHEMATICS
Academic year when starting the degree: 
Academic year in which the course will be held: 
Course type: 
Supplementary compulsory subjects
First Semester
Standard lectures hours: 
Detail of lecture’s hours: 
Lesson (64 hours)

Essential prerequisite in order to follow the course with profit is the mastery of the topics covered in the course of Probability.

Final Examination: 

There is only a final exam, which ensures the acquisition of knowledge through a written test and an oral test. The written exam will have duration of two hours, without using notes or books, tables (where necessary for the conduct of the written test will be provided along with the exam text); the test consists of two exercises, divided in multiple points, and an application of theory. For each are awarded 12 points and for the question of theory 6 points, to be admitted to the oral test is necessary to achieve the minimum score of 18, of which at least 4 points for the question of theory. After the correction of the written exam, students who have achieved sufficiency are asked to support the oral examination. This is structured as follows:-a review of the written exam in which you explain the fixes, you receive any student details and decide whether to change the written exam; -an oral examination, in order to check the knowledge regarding the theory lesson and facing the capacity of synthesis of this knowledge. The oral exam provides 10 points in positive or in negative.

Voto Finale

The student will learn the basic concepts of Bayesian statistics and will be able to wield the tools learned in the course. Return a description of the knowledge, skills and abilities that the student must demonstrate that they have acquired at the end of the course, possibly referring to the Dublin descriptors.

Bayesian approach to inferences is becoming increasingly important in various areas of statistics. The aim of the course is to introduce this approach to prametrical statistical inference problem. The main topics are: recalls and additions on probability theory; introduction to statistical survey methods; the Bayesian paradigm and bayesian statistical models; methods for assigning a priori distributions; hierarchical models; Gaussian hierarchical models and variance analysis; some asymptotic results; linear regression model and multiple linear regression.

- Box, George E. P.; Tiao, George C. “Bayesian inference in statistical analysis.”, Addison-Wesley Series in Behavioral Science: Quantitative Methods. Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1973. xviii+588 pp.
- Gelman, Andrew; Carlin, John B.; Stern, Hal S.; Dunson, David B.; Vehtari, Aki; Rubin, Donald B.
“Bayesian data analysis”. Third edition. Texts in Statistical Science Series. CRC Press, Boca Raton, FL, 2014. xiv+661 pp. ISBN: 978-1-4398-4095-5
- Ghosh, Jayanta; Delampady, Mohan; Samanta, Tapas. An introduction to Bayesian analysis. Springer Texts in Statistics. Springer, New York, 2006.
- Didier Dacunha-Castelle and Marie Duflo. Exercices de probabilités et statisti- ques. Tome 1. Collection Mathématiques Appliquées pour la Maitrise. [Collection of Applied Mathematics for the Master’s Degree]. Masson, Paris, 1982. Problèmes à temps fixe. [Problems with fixed time].
- Hoff, Peter D., A first course in Bayesian statistical methods. Springer Texts in Statistics. Springer, New York, 2009.
- Mark J. Schervish. Theory of statistics. Springer Series in Statistics. Springer- Verlag, New York, 1995.

Lectures for a total of 64 hours in the presence of the professor

Office hours: by appointment