B ayesian Computation
Yan Liu, Athula Abeyratne · 2019
This chapter introduces commonly used Bayesian computation methods, focusing on Markov chain Monte Carlo (MCMC) algorithms, including the Metropolis-Hastings algorithm and Gibbs sampling. It utilizes the discretization method to approximate Bayesian estimates of the shape and scale parameters in a Weibull distribution. The discretization method is not computationally efficient and much better estimates of the posterior distribution can be obtained using MCMC methods. The R package "coda" is used for output analysis (including generating the output summary statistics and plots) and MCMC diagnostics. The chapter also presents R and Just Another Gibbs Sampler example codes to explain the function of various portions of the codes, including creating and running the model, summarizing posterior samples, and different methods of MCMC chain convergence diagnostics. There are simpler but effective information-based methods available for model comparison. These are commonly known as penalized likelihood criteria (information criteria).