96794 - STATISTICAL INFERENCE AND MODELLING

Learning outcomes

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.

Course contents

Prerequisites: definition of probability, events, random variables, probability distributions and related quantities, law of large numbers, central limit theorem.

Part I - Statistical Inference

• Estimators: definition, properties, point estimate, interval estimation;
• Hypothesis testing: framework, type of errors, test statistics, parametric tests;
• Likelihood: definition, properties, maximum likelihood estimation, likelihood ratio test;
• [tentative] Resampling and bootstrap

Part II - Statistical Modeling

• Simple linear regression: model definition, estimation, goodness-of-fit, OLS strategy, properties of OLS, hypothesis testing, prediction;
• Multiple linear regression: model definition, estimation, goodness-of-fit, OLS strategy, properties of OLS, hypothesis testing, prediction;
• Model selection and diagnostics: strategies, cross-validation (intuition), dataset splitting, some criteria;
• Advanced regression techniques: [tentative] regularization.

Readings/Bibliography

Books are not mandatory but highly recommended.

• slides/material from the teacher
• (part I) "Statistics - Principles and Methods", Cicchitelli, G., D'Urso, P., Minozzo, M.
• (part I) "Statistical Inference", Casella, G., Berger, R.L.
• (part II) "An Introduction to Statistical Learning", Gareth, J., Witten, D., Hastie, T., and Tibshirani, R. [freely available online]
• (part II) "Applied linear statistical models", Kutner, M., Nachtsheim, C., Neter, J., Li, W. [freely available online]
• (part II) "A modern approach to regression with R", Sheather, S.J. [freely available online]

Teaching methods

Frontal teaching and lab lectures.

Assessment methods

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

Midterm exams are calibrated for 60 minutes duration.

Full exams are calibrated for 120 minutes duration.

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 (both practical and with software).

Teaching tools

Additional slides, as well as scripts used in lab lectures, will be provided by the teacher at virtuale.unibo.it.

Office hours

See the website of Saverio Ranciati