INTRODUCTION
The growth in the application of Bayesian analysis in the sciences has created a need to present its complex concepts in a more understandable language for non-statisticians. To many amateur users, their computationally-intensive simulation approaches has the appearance of a “black box”. This article aims to describe essential approaches used in Bayesian methods for posterior simulation in an intuitive manner. Four Bayesian computational methods are presented: Importance Sampling (IS) , Rejection sampling (RS), Markov Chain Monte Carlo (MCMC) and Data Augmentation (DA) . In this study, we aim to provide a comprehensive, yet easy to follow explanation of these techniques to make them practical for researchers. Some illuminating examples are presented to illustrate the algorithms and the concepts they embody. R software code and some other information are available in the Supplementary file as well.