BERGAMO
Dati Generali
Periodo di attività
Syllabus
Obiettivi Formativi
At the end of the course, students will be able to:
- understand the basic principles of Bayesian statistical inference;
- formulate simple Bayesian models using prior, likelihood and posterior distributions;
- perform conjugate Bayesian analysis in standard models;
- understand the role of Monte Carlo and Markov Chain Monte Carlo methods in Bayesian computation;
- interpret Bayesian hierarchical models and understand their usefulness in applied problems;
- formulate and interpret linear regression models for inference and prediction;
- understand the basic principles of supervised learning;
- apply logistic regression models for binary classification problems;
- critically interpret statistical outputs and assess model results;
- implement the main methods using statistical software, preferably R.
Prerequisiti
Metodi didattici
The exam consists of:
- a test including open-ended and multiple-choice questions, concerning theoretical topics or short applications of the methods studied;
- exercises to be solved also using the R software, aimed at evaluating the student’s ability to analyse different kinds of data and interpret statistical outputs.
The exam includes both a theoretical and a practical component. A positive evaluation of the theoretical part is required to pass the exam.
Some practical exercises may also be assigned as take-home work, possibly in the form of a short project.
Verifica Apprendimento
The exam consists of:
- a test including open-ended and T/F questions (concerning theoretical topics or short applications of the studied methods);
- exercises to be solved also by using the R software (to evaluate the student's ability to analyze different kinds of data and interpret statistical outputs).
Some practical exercises may also be assigned as take-home work, possibly in the form of a short project.
The two parts of the exam (theoretical and practical) both contribute to the total score, and both should be passed with a positive grade. A positive evaluation of the theoretical part is required to pass the exam.
The instructor reserves the right to require an additional oral examination, including after the written exam has taken place, whenever this is deemed necessary to verify the actual acquisition of the knowledge and skills required by the course learning objectives and to ensure the correct attribution of the final grade.
Contenuti
The data deluge faced by contemporary society poses new challenges to modern empirical sciences and calls for a strong interaction between statistics, machine learning, information science and computer science. In this context, Statistics plays a crucial role in providing principled methods for modelling uncertainty, drawing inference from data, and making predictions.
The course aims to highlight the role of statistical modelling in modern Data Science. It is organized into two main parts. The first part provides a gentle introduction to the Bayesian approach to statistics, with emphasis on the interpretation of prior and posterior distributions, conjugate models, computational methods, and hierarchical modelling. Particular attention is devoted to the computational challenges of Bayesian inference and to the advantages of the Bayesian framework for inference and prediction.
The second part introduces basic concepts of supervised learning, focusing on linear regression models for inference and prediction and logistic regression models for classification. These topics are mainly discussed within the Bayesian framework, while also emphasizing their role in applied statistical modelling.
Altre informazioni
- Documentation about R software is available at the following link: https://www.r-project.org/other-docs.html.