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
- Basic Concepts and Models
- Normal Approximation
- Hierarchical Models
- Model Checking
Part II: Bayesian Computations
- Introduction to Bayesian Simulation
- Sampling From Unknown Distribution
- Introduction to Markov chain Monte Carlo | R Code: Metropolis Metropolis-Hastings within Gibbs
- Monte Carlo Methods with Details
- Gibbs Sampler and Beyond
Part III: Advanced Bayesian Modeling
- Bayesian Regression and Shrinkage
- Bayesian Variable Selection | Related Paper
- Bayesian Nonparametric Modeling | R Regression Spline Code | Related Paper
- Bayesian Mixture Models
- 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.