Examples
Worked examples and illustrations for each chapter
Chapter 1: Basics of Bayesian inference
- Common univariate distributions (Chapter 1.1.1)
- Multivariate normal distribution (Chapter 1.1.3)
- Joint distribution for the beta-binomial example (Chapter 1.2.2)
- Bivariate posterior distribution (Chapter 1.5.3)
- Posterior predictive distribution (Chapter 1.6)
Chapter 2: From prior information to posterior inference
- Beta-binomial analysis of ESP data (Chapter 2.1.1)
- Poisson-gamma analysis of NFL concussions (Chapter 2.1.2)
- Normal-normal analysis of blood alcohol content (Chapter 2.1.3)
- Gaussian-Inverse Wishart analysis of marathon speeds (Chapter 2.1.7)
Chapter 3: Computational approaches
- Bayesian Central Limit Theorem Approximation (Chapter 3.1.3)
- Variational Bayes (Chapter 3.1.4)
- Gibbs sampling for the concussions data (Chapter 3.2.1)
- Gibbs sampling for a one sample t-test (Chapter 3.2.1)
- Gibbs sampling for the two-sample t-test (Chapter 3.2.1)
- Gibbs sampling for simple linear regression (Chapter 3.2.1)
- Metropolis sampling for the concussions data (Chapter 3.2.1)
- Metropolis sampling for the concussions data with adaptive tuning (Chapter 3.2.1)
- Metropolis + Gibbs sampling for simulated data (Chapter 3.2.1)
- Approximate Bayesian Computing (Chapter 3.2.2)
- Simulation Bayesed Inference (Chapter 3.2.3)
- Using JAGS for MCMC sampling (Chapter 3.3)
- Using JAGS for concussions data (Chapter 3.3)
- Using JAGS for the T-rex data (Chapter 3.3)
- Understanding error messages in JAGS (Chapter 3.3)
- Convergence diagnostics for a ill-posed model (Chapter 3.4)
- Convergence diagnostics for a well-behaved model (Chapter 3.4)
Chapter 4: Linear models
- One-sample t-test (Chapter 4.1)
- two-sample t-test (Chapter 4.1)
- Multiple linear regression for the homes data (Chapter 4.2)
- Logistic regression for NBA free throws (Chapter 4.3)
- Beta regression for the microbiome data (Chapter 4.3)
- Random effects model for the jaw bone data (Chapter 4.4)
- Random slopes model for the jaw bone data (Chapter 4.5)
- Random effects logistic regression for the Gambia data (Chapter 4.5)
- Spatial modeling of gun-related homicide rates (Chapter 4.6)
Chapter 5: Hypothesis testing
- Bayesian multiple testing (Chapter 5.2)
- AB testing (Chapter 5.3)
- Bayesian bandit with Thompson sampling (Chapter 5.3)
- Power calculation (Chapter 5.4)
Chapter 6: Model selection and diagnostics
- Cross validation (Chapter 6.1)
- Stochastic search variable selection (Chapter 6.2)
- Model selection with DIC/WAIC for the Gambia data (Chapter 6.4)
- DIC/WAIC simulation study (Chapter 6.4)
- Bayesian p-values for the Guns laws data (Chapter 6.5)
Chapter 7: Case studies using hierarchical modeling
- Hidden Markov modeling (Chapter 7.1.2)
- Missing data analysis of 2016 Boston marathon data (Chapter 7.1.4)
- Species distribution mapping via data fusion (Chapter 7.2.1)
- Analysis of tyrannosaurid growth curves (Chapter 7.2.2)
- Climate reconstruction using proxy data (Chapter 7.2.3)
Chapter 8: Machine learning
- Variable selection for high-dimensional data (Chapter 8.1)
- Continuous shrinkage priors (Chapter 8.1)
- Bayesian linear regression for hurricane forecasting (Chapter 8.3)
- Spline regression for the motorcycle data (Chapter 8.3.1)
- Generalized additive modeling for hurricane forecasting (Chapter 8.3.1)
- Gaussian process regression illustration (Chapter 8.3.2)
- Bayesian adaptive regression trees for hurricane forecasting (Chapter 8.3.3)
- Feed-forward neural network for hurricane forecasting (Chapter 8.3.4, MCMC code)
- Heteroskedastic regression (Chapter 8.4.1)
- Toy example of density regression (Chapter 8.4.2)
- Interpretable machine learning for hurricane forecasting (Chapter 8.5)
- Toy example of causal inference (Chapter 8.6.1)
- Semiparametric Bayesian quantile regression (Chapter 8.6.3, MCMC code)
Chapter 9: Statistical properties of Bayesian methods
- Simulation study for the Bayesian LASSO (Chapter 9.3)
- Simulation study for variational Bayes (Chapter 9.3)