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STATISTICS A

Degree course: 
Corso di Second cycle degree in MATHEMATICS
Academic year when starting the degree: 
2021/2022
Year: 
1
Academic year in which the course will be held: 
2021/2022
Course type: 
Supplementary compulsory subjects
Credits: 
8
Period: 
Second semester
Standard lectures hours: 
64
Detail of lecture’s hours: 
Lesson (64 hours)
Requirements: 

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

Final Examination: 
Orale

There is a final examination to ascertain the acquisition of knowledge through an oral test in which the student will present a paper (15-20 min) from which questions on the course content will be taken.

Assessment: 
Voto Finale

The student will learn the basic concepts of Bayesian statistics and will be able to wield the tools learned in the course.

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: introduction to statistical survey methods; the Bayesian paradigm and bayesian statistical models; methods for assigning a priori distributions; hierarchical models; Gaussian hierarchical model; linear regression model. Monte Carlo and Markov chain Monte Carlo simulation

The main topics covered are: introduction to statistical survey methods: sampling, estimation and hypothesis testing; the Bayesian paradigm with examples: Bernoulli and Gaussian models; methods for assigning an a priori distribution; hierarchical models with examples; the linear regression model. Monte Carlo and Markov chain Monte Carlo type algorithms: Metropolis-Hastings and Gibbs Sampler

- 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.

Convenzionale

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

Office hours: by appointment

Professors

MIRA ANTONIETTA

Borrowers