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 in an effective and coherent way.

Course contents

1. Short review of fundamental concepts of probability
2. Moment generating Functions and Characteristic Functions
3. Convergence of random variables
4. Introduction to Bayesian and frequentist statistical inference: models and learning
5. Parametric inference: method of moments, maximum likelihood and properties
6. Optimization methods for maximum likelihood, EM algorithm
7. Hypothesis testing and p-values: the Wald test, Chi-square distribution, Likelihood Ratio Test, Multiple Testing
8. Nonparametric hypothesis testing about one and two samples
9. Simulation and permutation tests
10. Bootstrap

Readings/Bibliography

Used course material consists of lecture notes and slides provided by the teacher.

Background information can be found in several chapters of the following books:

• George Casella, Roger L. Berger, Statistical Inference, 2^nd Edition, 2002, Duxbury Pr (Cengage)
• All of Statistics, A Coincise Course in Statistical Inference, Larry Wasserman, Springer.

 

Teaching methods

Lectures and tutorials

Assessment methods

The learning assessment is determined by two components:

1. Fifteen points are assigned to regular homework activities. Throughout the course, five individual homework assignments will be given. These assignments will consist of exercises or data analysis projects developed using R.

2. Eighteen points are allocated to a two-hour exam comprising both theoretical and practical exercises, aimed at assessing the students' ability to apply the learned definitions, properties, and theorems. During the written exam, students are allowed to use the textbook, personal notes, and a calculator. However, the use of mobile phones, smartwatches, or similar electronic data storage or communication devices is strictly prohibited. The written exam consists of a quiz comprising multiple-choice questions with four possible answers.

The final grade is determined by the sum of these two components. A total score of 33 or 34 corresponds to a grade of 30 with honors (Laude).

 

Teaching tools

Blackboard and slides

Office hours

See the website of Cinzia Viroli