First cycle
degree courses
Second cycle
degree courses
Single cycle
degree courses
School of Science
Course unit
SCP4063084, A.A. 2019/20

Information concerning the students who enrolled in A.Y. 2019/20

Information on the course unit
Degree course Second cycle degree in
SS1736, Degree course structure A.Y. 2014/15, A.Y. 2019/20
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Number of ECTS credits allocated 9.0
Type of assessment Mark
Course unit English denomination STATISTICS (ADVANCED)
Website of the academic structure
Department of reference Department of Statistical Sciences
E-Learning website
Mandatory attendance No
Language of instruction Italian
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Teacher in charge NICOLA SARTORI SECS-S/01

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Core courses SECS-S/01 Statistics 9.0

Course unit organization
Period Second semester
Year 1st Year
Teaching method frontal

Type of hours Credits Teaching
Hours of
Individual study
Practice 2.0 26 24.0 No turn
Lecture 7.0 56 119.0 No turn

Start of activities 02/03/2020
End of activities 12/06/2020
Show course schedule 2019/20 Reg.2014 course timetable

Examination board
Board From To Members of the board
6 Commissione a.a.2019/20 01/10/2019 30/09/2020 SARTORI NICOLA (Presidente)
SALVAN ALESSANDRA (Membro Effettivo)

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
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; Neyman-Pearson 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
- 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
- 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: Springer-Verlag Italia, 2001. Cerca nel catalogo
  • Luigi Pace & Alessandra Salvan, Introduzione alla statistica - II - Inferenza, verosimiglianza, modelli. Padova: Cedam, 2001. Cerca nel catalogo