Bayesian Data Analysis

If I should ever have a tattoo, that would be

$$p(\theta|y)= \frac{p(y|\theta)p(\theta)}{p(y)}$$

Mattias Villani

Prerequisites

Literature

Part I: Bayesian Theory and Models

  1. Introduction
  2. Basic Concepts and Models
  3. Normal Approximation
  4. Hierarchical Models
  5. Model Checking

Part II: Bayesian Computations

  1. Introduction to Bayesian Simulation
  2. Sampling From Unknown Distribution
  3. Introduction to Markov chain Monte Carlo | R code
  4. Monte Carlo Methods with Details
  5. Gibbs Sampler and Beyond

Part III: Advanced Bayesian Modeling

  1. Bayesian Regression and Shrinkage
  2. Bayesian Variable Selection | Related Paper
  3. Bayesian Nonparametric Modeling | R Regression Spline Code | Related Paper
  4. Bayesian Mixture Models
  5. Bayesian Copula Modeling | R copula and VineCopula packages

Software

Computer code

External Reading

If you have good command of elementary statistics, this is a good first book for someone who is interested in practical uncertainty quantification, that would like to learn about the Big Picture. It is a book about thinking and working like a Bayesian, rather than about techniques of Bayesian estimation.