
Course unit
STATISTICS (ADVANCED)
SCP4063084, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Core courses 
SECSS/01 
Statistics 
9.0 
Course unit organization
Period 
Second semester 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Practice 
2.0 
26 
24.0 
No turn 
Lecture 
7.0 
56 
119.0 
No turn 
Prerequisites:

Probability Theory (Calcolo delle Probabilità). Strong background in Calculus and Linear Algebra. 
Target skills and knowledge:

Knowledge: essential statistical toolbox for the understanding and solving of problems in methodological Statistics.
Skills: ability to recognize the statistical toolbox used in different statistical contexts; ability to solve simple methodological problems and to understand or formulate suitable models for their description. 
Examination methods:

Written closed book exam. Details on the exam rules will be available in the Moodle page of the course (at https://elearning.unipd.it) 
Assessment criteria:

Esam with exercises, each formed of several questions of similar difficulty. 
Course unit contents:

 Model specification and evaluation of inferential uncertainty. Paradigms of inference: frequentist and Bayesian.
 Common families of distributions.
 Elements of statistical inference (review): point estimation, confidence intervals, hypotheses testing.
 The likelihood function: definition, examples and properties (invariance, Wald inequality). Likelihood quantities: definition (score function, observed and expected information) and properties.
 Sufficient statistics.
 Maximum likelihood estimation: definition, examples and properties (equivariance, consistency, asymptotic normality).
 Likelihood ratio tests: definition and examples; asymptotic distribution and asymptotic equivalent tests; confidence regions based on the likelihood ratio.
 Profile likelihood.
 Bayesian inference: Bayes theorem; prior distributions and conjugate families; examples; asymptotic approximations; point estimation; credibility regions and hypotheses testing.
 Optimality theory: Cramer Rao inequality; uniformly minimum variance unbiased (UMVU) estimators; NeymanPearson lemma. Uniformly most powerful (UMP) tests; Bayesian optimality.
 Model misspecification and estimating equations.
 
Planned learning activities and teaching methods:

Upfront classes: theory (75%), exercises (25%).
Support by: Sevizio tutorato. 
Additional notes about suggested reading:

Suggested reading list:
 Adimari, G., Pauli, F. (2012). Esercizi di Statistica (corso progredito).
(disponibile gratuitamente in formato pdf all'indirizzo https://homes.stat.unipd.it/sites/homes.stat.unipd.it.gianfrancoadimari/files/libro_eserc.pdf)
 Casella, J., Berger, R.L. (2001). Statistical Inference (2nd edition). Duxbury Press.
 Evans, M.J., Rosenthal, J.S. (2003). Probability and Statistics: The Science of Uncertainty. W.H. Freeman and Co. (disponibile gratuitamente in formato pdf all'indirizzo http://www.utstat.toronto.edu/mikevans/jeffrosenthal/)
 Gelman, A., Carlin, J.B., Stern, H.S., Dunson, D.B., Vehtari, A., Rubin, D.B. (2014). Bayesian Data Analysis (3rd edition). CRC Press. 
Textbooks (and optional supplementary readings) 

Adelchi Azzalini, Inferenza statistica: una presentazione basata sul concetto di v. MIlano: SpringerVerlag Italia, 2001.

Luigi Pace & Alessandra Salvan, Introduzione alla statistica  II  Inferenza, verosimiglianza, modelli. Padova: Cedam, 2001.


