ABSTRACT
Bayesian inference statements stem from the data-informed knowledge distribution of the unknown quantities in the model. This chapter introduces analytical, asymptotic and Monte Carlo sampling methods, respectively. It discusses the ground-breaking Gibbs sampling method and its generalization, Markov chain Monte Carlo. The chapter deals with the issue of whether or not the Markov chain generated samples can be considered as “random” samples from the target distribution. Historically, large-sample approximations have played an important role in statistics. Most statistical software packages have routines that will find the posterior mode vector and covariance matrix. Simulating samples from a distribution requires random number generation. Most statistical packages provide one or more random number generators, along with several functions to simulate from common families of distributions.
