- Docente: Elena Bandini
- Credits: 6
- SSD: MATH-03/B
- Language: Italian
- Teaching Mode: In-person learning (entirely or partially)
- Campus: Bologna
- Corso: First cycle degree programme (L) in Mathematics (cod. 6061)
Learning outcomes
The aim of the course is to give students the basic knowledge of mathematical statistics, in particular point estimation, interval estimation and hypothesis tests. In the end of the course, the student possesses the ability to apply such statistical methods to other mathematical and applied areas.
Course contents
Point estimators: definition and basic properties, method of moments, maximum likelihood method.
Methods for evaluating estimators: mean squared error and UMVU estimators, sufficient statistic, complete statistic, Lehmann–Scheffé theorem, Cramér–Rao theorem, efficiency properties.
Confidence intervals: construction of a confidence interval, optimal confidence intervals, and asymptotic confidence intervals.
Hypothesis testing: how to find a hypothesis test, likelihood ratio test, error probabilities and power function, randomized tests, UMP tests, tests for comparing means, tests for comparing proportions.
Elements of Bayesian statistics: point estimators, conjugate families, main Bayesian estimators, improper prior distributions.
Readings/Bibliography
Lecture notes and exercise sheets provided by the instructor, available on the virtuale.unibo.it platform.
Supplementary textbook:
G. Casella and R. Berger, Statistical Inference, Duxbury, Thomson Learning, Second edition, 2001.
Teaching methods
Theoretical lectures and practical sessions will alternate in order to clarify the theory covered as much as possible through examples.
Assessment methods
Learning assessment will be carried out solely through the final examination, which verifies the acquisition of the expected knowledge and skills through an oral exam on exercises and theory.
Teaching tools
The course website is available on the virtuale.unibo.it platform, where students can find the course lecture notes, exercise sheets, and other useful information about the course.
Office hours
See the website of Elena Bandini