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. Basic introduction to asymptotic theory.
Linear regression. Nonconjugate priors and Metropolis-Hastings algorithms. Linear and generalized mixed effect models. Methods for ordinal data. Semi-parametric regression and mixture 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 an oral 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. Mixutre models: a basic introduction and non-parametric approaches (time permitting).