Digesting Gibbs Sampling Using R

TL;DR

This paper provides a practical framework for implementing Gibbs sampling, a specific MCMC technique, aimed at users interested in statistical simulation without delving into complex proofs.

Contribution

It offers a user-oriented guide to Gibbs sampling within the broader context of Monte Carlo methods, emphasizing implementation over theoretical proofs.

Findings

Framework for Gibbs sampling implementation

Simplified explanation without proofs

Accessible to users with basic calculus and statistics knowledge

Abstract

In general, the statistical simulation approaches are referred to as the Monte Carlo methods as a whole. The broad class of the Monte Carlo methods involves the Markov chain Monte Carlo (MCMC) techniques that attract the attention of researchers from a wide variety of study fields. The main focus of this report is to provide a framework for all users who are interested in implementing the MCMC approaches in their investigations, especially the Gibbs sampling. I have tried, if possible, to eliminate the proofs, but reader is expected to know some topics in elementary calculus (including mathematical function, limit, derivative, partial derivative, simple integral) and statistics (including random variables, expected value and variance, moment generating function, multivariate distribution, distribution of a functions of random variable, and the central limit theorem).