- Docente: Silvia Cagnone
- Credits: 6
- SSD: SECS-S/01
- Language: English
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: First cycle degree programme (L) in Statistical Sciences (cod. 8873)
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from Nov 06, 2023 to Dec 14, 2023
Learning outcomes
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.
Course contents
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.
Readings/Bibliography
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.
Teaching methods
Lectures and tutorials
Assessment methods
The exam consists of a mandatory written exam (lasting two hours).
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.
During the exam the use of textbooks, notes and computers tools are not allowed.
Teaching tools
Slides available at https://virtuale.unibo.it
Office hours
See the website of Silvia Cagnone