85159 - Fundamental Concepts of Statistics

Learning outcomes

By the end of the course the student acquires the fundamental notions of theory of probability and statistical inference. In particular, the student is able to investigate the properties of random variables, including transformations and convergence, and to solve estimation problems and hypothesis testing by classical parametric inference and bootstrap in an effective and coherent way.

Course contents

1. Fundamental concepts of probability: univariate and multivariate random variables, conditional and marginal distributions, independent random variables
2. Transformations of univariate and multivariate random variables
3. Moment generating Functions and Characteristic Functions
4. Inequalities
5. Convergence of random variables
6. Introduction to statistical inference: models and learning
7. Parametric inference: method of moments, maximum likelihood and properties, optimization methods and the EM algorithm
8. Hypothesis testing and p-values: the Wald test, Chi-square distribution, Likelihood Ratio Test, Multiple Testing

Readings/Bibliography

George Casella, Roger L. Berger, Statistical Inference, 2nd Edition, 2002, Duxbury Pr (Cengage), ISBN: 9780534243128

Teaching methods

Lectures and tutorials

Assessment methods

The learning assessment is composed by a written test lasting 2 hours, followed by an oral examination. The written test is aimed at assessing the student's ability to use the learned definitions, properties and theorems in solving theoretical exercises. During the written exam, students can make use of the text book, personal notes and a calculator. Students are not permitted to use a mobile phone (and smart watch or similar electronic data storage or communication device). The written test consists of some exercises articulated in several points with a final grade out of thirty.

Teaching tools

Blackboard and slides

Office hours

See the website of Cinzia Viroli