This Element introduces the basics of Bayesian regression modeling using modern computational tools. This Element only assumes that the reader has taken a basic statistics course and has seen Bayesian inference at the introductory level of Gill and Bao (2024). Some matrix algebra knowledge is assumed but the authors walk carefully through the necessary structures at the start of this Element. At the end of the process readers will fully understand how Bayesian regression models are developed and estimated, including linear and nonlinear versions. The sections cover theoretical principles and real-world applications in order to provide motivation and intuition. Because Bayesian methods are intricately tied to software, code in R and Python is provided throughout.
Muu info
This Element is an introduction to Bayesian regression, combining theory and application with R and Python code for learners.
1. Introduction: the purpose and scope of this element;
2. A review of
Bayesian principles and inference;
3. Monte Carlo tools for computational
power;
4. A simple introduction to the mathematics of Markov Chains;
5.
Markov Chain Monte Carlo for estimating Bayesian models;
6. Basic Bayesian
regression models;
7. Nonlinear Bayesian regression models;
8. Model
evaluation and mechanical issues with MCMC estimation;
9. Final remarks;
References.
