96794 - Statistical Inference and Modelling

Learning outcomes

The goal of the course is to provide students with the theoretical knowledge about the likehood function, its properties, its use in statistical inference and how to numerically maximize it. Moreove, by the course the student acquires fundamentals of modeling, with special attention to models and methods that address practical data issues. At the end of the course, students are expected to be able: to setup and perform statistical analysis based on principled methods, using inferential tools which are appropriate for the applied real data situation; 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. estimators: definition, properties, point estimate, interval estimation; hypothesis testing: framework, type of errors, test statistics, parametric tests.

Part I - Statistical Inference

Likelihood: definition and likelihood principle; sufficient statistics and minimal sufficient statistics; exponential families; maximum likelihood; numerical maximization of the likelihood; observed and expected information; Rao-Cramér inequality; maximum likelihood estimators and their properties; likelihood ratio test.

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.

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.

"Students attending labs, due to research or teaching activities, are considered in terms of safety as staff members of the universities and thus have to attain specific online certifications provided at the link below."

Link

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).

AI policy: during the exam is strictly forbidden to use any AI tool, either for solving the exercises or producing the comments of the output. Any violation will result in an immediate termination of the exam attempt.

 

Students with learning disorders and\or temporary or permanent disabilities: please, contact the office responsible (https://site.unibo.it/studenti-con-disabilita-e-dsa/en/for-students ) as soon as possible so that they can propose acceptable adjustments. The request for adaptation must be submitted in advance (15 days before the exam date) to the lecturer, who will assess the appropriateness of the adjustments, taking into account the teaching objectives.

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