Bayesian Computation with R Notebooks

Jim Albert, Fall 2013

One Parameter Models

• Sequential learning by Bayes rule
• Learning about a proportion using a discrete prior
• Brute-force Bayes computation for a single parameter
• Learning about a proportion - Part I
• Learning about a proportion - Part II
• Learning about a proportion - Part III

Multiparameter Models

• Inference about a normal distribution - Part I
• Inference about a normal distribution - Part II
• Inference with Cauchy sampling
• Inference about a normal population with grouped data

Bayesian Computation

• Illustration of Metropolis-Hastings random walk for Cauchy sampling
• Exponential decay regression model using LearnBayes and JAGS
• Computation of a mixture-of-exponentials sampling model
• Laplace method for zero-inflated Poisson model
• Laplace method zero-inflated model - slideshow

Hierarchical Models

• Heart transplant (Poisson/Gamma) example using JAGS and LearnBayes
• Comparison of two exchangeable models
• Binomial/beta model for school testing data
• Exchangeable modeling of career trajectories

Bayes Testing

• Posterior predictive checking to check for overdispersion
• Normal testing examples
• Bayes factors to compare two binomial/beta models
• Two Bayes factor examples
• Test of the equiprobability of a multinomial vector
• Box's method for assessing data/prior conflict

Regression

• Normal linear regression
• Logistic regression - oring example
• Probit regression fitting using data augmentation