Università degli Studi di Pavia

Dipartimento di Matematica ''F. Casorati''

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Elements of Mathematical Statistics

Professors:
Bassetti Federico
Year:
2015/2016
Course code:
504505
ECTS:
6
SSD:
MAT/06
DM:
270/04
Lessons:
56
Period:
I semester
Language:
Italian

Objectives

Introduction to mathematical statistics, bayesian and frequentistic.

Teaching methods

Lectures

Examination

written and oral examinations

Prerequisites

Probability, linear algebra, calculus

Syllabus

-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