Overview of main concepts of Bayesian Statistics: parametric inference, predictive inference, univariate parametric models, Monte Carlo methods.
In depth study of techniques for model checking and selection.
Linear regression. Nonconjugate priors and Metropolis-Hastings algorithms. Linear and generalized mixed effect models. Methods for ordinal data. Semi-parametric regression and non-parametric models.
Peter D. Hoff A First Course in Bayesian Statistical Methods, 2009 Springer
Bayesian Data Analysis, 3rd ed, by Andrew Gelman, John Carlin, Hal Stern, David Dunson, Aki Vehtari, and Donald Rubin. (http://www.stat.columbia.edu/~gelman/book/).
Learning Objectives
KNOWLEDGE: Deep understanding of Bayesian inference techniques for data analysis.
EXPERTISE: Students will be trained to analyze data using a range of Bayesian models, perform model selection and criticism
ACHIEVED ABILITIES AT THE END
OF THE COURSE: Students will be able to develop and implement a Bayesian statistical model involving simple and complex dependencies, implement and/or use advanced computational techniques
Prerequisites
Preparatory courses: Statistical inference, Probability and mathematics for statistics, Bayesian statistics
Teaching Methods
Oral lectures and sessions of exercises
Further information
Intermediate knowledge of the R software is required
Type of Assessment
There will be a written exam (1/3 of the final mark); homeworks (1/3) and final project (1/3).
Course program
Overview of the main aspects of Bayesian inference: parametric models, HPD regions, predictive inference, conjugate families, non-informative priors, Jeffreys priors, Monte Carlo methods.
Introduction to the statistical software Stan.
In depth coverage of tools for model assessment/checking, and selection.
Regression methods and variables selection. G-priors. Hierarchical models, linear hierarchical models Bayesian generalized linear models. Semi-parametric (non-linear) regression. Nonparametric models based on Dirichlet processes: a basic introduction.