# 96794 - STATISTICAL INFERENCE AND MODELLING

## Conoscenze e abilità da conseguire

By the course the student acquires fundamentals of statistical inference and modeling, with special attention to models and methods that address practical data issues. At the end of the course the student is able: - to define generalized linear regression models; - to estimate parameters and test hypotheses about them - to choose the most suitable model for the specific problem at hand.

## Contenuti

The course is devided in two modules

[Module I- Inference] Saverio Ranciati

- Random Variables and Probability Distributions: definition and properties of r.v., univariate probability distributions; bivariate case, conditional and marginal distributions; multivariate distribution, the Gaussian case.

- Law of Large Numbers and Central Limit Theorem;

- Statistical Inference: definition of estimator, properties, point and interval estimation;

- Hypothesis testing: parametric and nonparametric tests;

- Likelihood: definition and Ratio Test;

- [Tentative] Resampling and Bootstrap.

[Module II- Statistical models] Angela Montanari

- Linear regression: estimation and hypothesis testing

- Linear model selection and regularization

- Generalized linear models and non linear models (basics)

## Testi/Bibliografia

• Cicchitelli, G., D'Urso, P., Minozzo, M. "Statistics - Principles and Methods", ed. Pearson, 2021;
• Casella, G., Berger, R.L. "Statistical Inference", ed. Cengage Learning, 2002 (or any edition).
• Gareth, J., Witten, D., Hastie, T., and Tibshirani, R., An Introduction to Statistical Learning (June 2013), Springer
Book Homepage [http://www.statlearning.com/]
pdf (9.4Mb, 6th corrected printing) [http://www-bcf.usc.edu/~gareth/ISL/ISLR%20Sixth%20Printing.pdf]

• Kutner, M., Nachtsheim, C., Neter, J., Li, W., Applied linear statistical models, McGraw-Hill, 2004

## Metodi didattici

Frontal teaching and lab lectures.

## Modalità di verifica e valutazione dell'apprendimento

Midterm exams - at the end of lectures of Module I and of Module II- or Full exam at the end of the course.

Final mark is the average of two midterms (Module I + Module II) or a single evaluation on the full exam.

Type of exam: written, multiple choices and open questions with exercises.

## Strumenti a supporto della didattica

Scripts used in lab lectures will be provided by the teacher at virtuale.unibo.it

## Orario di ricevimento

Consulta il sito web di Angela Montanari

Consulta il sito web di Saverio Ranciati