Elements of mathematical stati
- Professors:
- Bassetti Federico
- Year:
- 2014/2015
- Course code:
- 504505
- ECTS:
- 6
- SSD:
- MAT/06
- DM:
- 270/04
- Lessons:
- 56
- Language:
- Italiano
Objectives
Introduction to mathematical statistics, bayesian and frequentistic.
Teaching methods
Lectures
Examination
written and oral examinations
Prerequisites
Probability, linear algebra, calculus
Syllabus
Introduction to mathematical statistics
-Basic examples (gaussian samples, binomial models)
-Maximum likelihood estimators
-Sufficient statistics, complete statistics, factorization theorem
-unbiased estimators. UMVUE.
-exponential families
-basic asymptotic theory
-confidence interval
-testing statistical hypothesis
-Neyman-Pearson tests
-goodness of fit test
-linear regression, anova
-basic bayesian statistics (prior, posterior, predictive distributions)
-decision theory
-exponential families for bayesian inference
-conjugate priors
-linear model (BLUE, Gauss-Markov theorem, gaussian linear model, MLE, test)
-Basic examples (gaussian samples, binomial models)
-Maximum likelihood estimators
-Sufficient statistics, complete statistics, factorization theorem
-unbiased estimators. UMVUE.
-exponential families
-basic asymptotic theory
-confidence interval
-testing statistical hypothesis
-Neyman-Pearson tests
-goodness of fit test
-linear regression, anova
-basic bayesian statistics (prior, posterior, predictive distributions)
-decision theory
-exponential families for bayesian inference
-conjugate priors
-linear model (BLUE, Gauss-Markov theorem, gaussian linear model, MLE, test)
Bibliography
-Bickel, P.J. and Doksum, K. A. Mathematical statistics, Holden-Day Inc.
Dipartimento di Matematica ''F. Casorati''
Università degli Studi di Pavia -
Via Ferrata, 5 - 27100 Pavia
Tel +39.0382.985600 - Fax +39.0382.985602