Syllabus del corso
Obiettivi formativi
The course aims to introduce the Bayesian approach, both from a theoretical and applied point of view, and to problems of inference related to longitudinal data, for repeated measures over time of same statistical units. The freeware statistical software R Project will be used for the applied part of the course.
Contenuti sintetici
Programma esteso
- Bayesian Statistics:
- Introduction: framework and priors
- Decision-theoretic foundations: evaluation of estimators and loss functions
- Priors: models, subjectivity, conjugacy and noninformativeness
- Bayesian point estimation: inference, normal model, dynamic models
- Bayesian calculations: approximation methods, Markov chain Monte Carlo
- Other topics: tests and model choice, hierarchical models, empirical Bayes
- Longitudinal data:
- Linear mixed models: mixed-effects models, fitting, parameter variability
- Multiple random-effect terms: crossed effects, nested effects, partially crossed effects
- Longitudinal models: models with correlated and uncorrelated effects, precision assessment, prediction
- Computational methods: framework, penalized least squares, residual maximum likelihood
Prerequisiti
There are no formal prerequisites, but basic knwoledge of the following topics is needed: Mathematical Analysis, Linear Algebra, Probability Calculus, Statistical Inference, R programming.
Metodi didattici
Theoretical and applied (with R statistical software) frontal lectures.
Modalità di verifica dell'apprendimento
The exam will be consist of a written test with exercises and open questions, to assess knowledge and autonomous reproduction of the study material proposed during the course.
In the exercises we will assess theoretical and applied aspects of the course, on how to correctly build, estimate and implement statistical models and inferential methodologies being studied.
In the open questions we will assess the capacity of the student in the interpretation of complex problems and in the communication of elaborated answers requiring formal reasoning, logic discretion, and coherente language.
No different exams will be provided between attending and no attending students.Testi di riferimento
There is no specific textbook.
Class notes will be provided during the course.
For the first part of the course, a good reference book is P.D. Hoff (2009) A First Course in Bayesian Statistical Methods, Springer https://www.stat.washington.edu/~pdhoff/book.php.
For the applied part of the course students are referred to the online material available available at http://www.r-project.org.
Periodo di erogazione dell’insegnamento
First semester
Lingua di insegnamento
English
Learning objectives
The course aims to introduce the Bayesian approach, both from a theoretical and applied point of view, and to problems of inference related to longitudinal data, for repeated measures over time of same statistical units. The freeware statistical software R Project will be used for the applied part of the course.
Contents
Introduction to Bayesian Statistics and to longitudinal data analysis
Detailed program
- Bayesian Statistics:
- Introduction: framework and priors
- Decision-theoretic foundations: evaluation of estimators and loss functions
- Priors: models, subjectivity, conjugacy and noninformativeness
- Bayesian point estimation: inference, normal model, dynamic models
- Bayesian calculations: approximation methods, Markov chain Monte Carlo
- Other topics: tests and model choice, hierarchical models, empirical Bayes
- Longitudinal data:
- Linear mixed models: mixed-effects models, fitting, parameter variability
- Multiple random-effect terms: crossed effects, nested effects, partially crossed effects
- Longitudinal models: models with correlated and uncorrelated effects, precision assessment, prediction
- Computational methods: framework, penalized least squares, residual maximum likelihood
Prerequisites
There are no formal prerequisites, but basic knwoledge of the following topics is needed: Mathematical Analysis, Linear Algebra, Probability Calculus, Statistical Inference, R programming.
Teaching methods
Theoretical and applied (with R statistical software) frontal lectures.
Assessment methods
The exam will be consist of a written test with exercises and open questions, to assess knowledge and autonomous reproduction of the study material proposed during the course.
In the exercises we will assess theoretical and applied aspects of the course, on how to correctly build, estimate and implement statistical models and inferential methodologies being studied.
In the open questions we will assess the capacity of the student in the interpretation of complex problems and in the communication of elaborated answers requiring formal reasoning, logic discretion, and coherente language.
No different exams will be provided between attending and no attending students.Textbooks and Reading Materials
There is no specific textbook.
Class notes will be provided during the course.
For the first part of the course, a good reference book is P.D. Hoff (2009) A First Course in Bayesian Statistical Methods, Springer https://www.stat.washington.edu/~pdhoff/book.php.
For the applied part of the course students are referred to the online material available available at http://www.r-project.org.
Semester
First semester
Teaching language
English
Scheda del corso
Staff
-
Stefano Peluso