If I should ever have a tattoo, that would be
- Basic knowledge of Statistics
- Basic knowledge of Statistical Computing
- Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2014). Bayesian data analysis (third edition), CRC press.
- Robert, C., & Casella, G. (2010). Introducing Monte Carlo Methods with R. Springer.
Part I: Bayesian Theory and Models
- L1: Introduction
- L2: Basic Concepts and Models
- L3: Normal Approximation
- L4: Hierarchical Models
- L5: Model Checking
- L6: Bayesian Regression and Shrinkage
- L7: Bayesian Variable Selection | Related Paper
Part II: Bayesian Computations
- L8: Introduction to Bayesian Simulation
- L9: Sampling From Unknown Distribution
- L10: Introduction to Markov chain Monte Carlo | R code
- L11: Monte Carlo Methods with Details
- L12: Gibbs Sampler and Beyond
Part III: Bayesian Advanced Modeling
- A1: Bayesian Nonparametric Modeling | R Regression Spline Code | Related Paper
- A2: Bayesian Mixture Models
- A3: Bayesian Copula Modeling | R copula and VineCopula packages
- Howson, C. and Urbach, P., 2006. Scientific reasoning: the Bayesian approach. third edition, Open Court Publishing.
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.