- Docente: Silvia Cagnone
- Crediti formativi: 6
- SSD: SECS-S/01
- Lingua di insegnamento: Inglese
- Modalità didattica: Convenzionale - Lezioni in presenza
- Campus: Bologna
- Corso: Laurea in Scienze statistiche (cod. 8873)
-
dal 07/11/2022 al 07/12/2022
Conoscenze e abilità da conseguire
By the end of the course the student should know the basic theory of likelihood-based and Bayesian statistical inference. In particular the student should be able: - to derive maximum likelihood and Bayesian estimators and their properties - to derive interval estimates - to test statistical hypotheses according to Neyman and Pearson’s approach and the GLR criterion.
Contenuti
Introduction to the statistical inference. The Likelihood function. Sufficient statistics.
Estimation theory.
Moments and maximum likelihood estimation method. Point estimation: finite and asymptotic properties of estimators. Interval estimation: the pivotal quantity method and asymptotical confidence intervals.
Hypothesis testing.
Neyman-Pearson theory. Null hypothesis and alternative hypothesis; Type I and Type II errors; power of a test. Rejection Region. Simple hypothesis and composite hypothesis. Simple null and alternative hypothesis: Neyman-Pearson's lemma. Generalized Likelihood Ratio Test.
Bayesian inference.
Subjective approach to probability. Bayesian estimation. Loss function appraoch. Conjugate prior distributions.
Testi/Bibliografia
Larsen R.J. and Marx M.L. "An introduction to mathematical statistics and its applications", Prentice Hall, 2012.
Azzalini A. "Statistical infernece based on the likelihood", Chapman & Hall/CRC, 2002.
Hoff P.D "A First Course in Bayesian Statistical Methods", Springer, 2009.
Metodi didattici
Lectures and tutorials
Modalità di verifica e valutazione dell'apprendimento
The exam consists of a mandatory written exam (lasting two hours) and an optional oral exam.
The exam paper consists of questions concerning the theoretical parts of the course and exercises aiming at evaluating if the students are able to solve statistical inference problems. The final grade is given by the sum of the partial grades obtained in each exercise and is expressed out of thirty.
The oral exam allows the student to increase or decrease the grade obtained in the written exam. In this case the final grade is obtained as the average between the written and the oral exam.
During the exam the use of textbooks, notes and computers tools are not allowed.
Strumenti a supporto della didattica
Slides available at https://virtuale.unibo.it
Orario di ricevimento
Consulta il sito web di Silvia Cagnone