ABSTRACT
This chapter provides an overview of Bayesian statistics and highlights the differences between the frequentist and Bayesian methods. Bayesian statistics is a branch of statistics founded upon Bayesian probability theory. In the Bayesian framework, the data distribution is defined by parameters, some of which are related to the question at hand. The key component of Bayesian inference is in the selection of prior distributions. Started in 1989, the Bayesian inference Using Gibbs Sampling (BUGS) language was among the first to provide a generic interface to Markov chain Monte Carlo sampling. Just Another Gibbs Sampler (JAGS) provides a similar user interface to the BUGS language so that nearly all BUGS code can be run in JAGS and vice versa with little editing. Both BUGS and JAGS are powered with expert software programming tricks and techniques to perform Metropolis–Hastings with a random-walk updater, Gibbs, and slice sampling.
