Teaching Markov Chain Monte Carlo: Revealing the Basic Ideas Behind the Algorithm

Abstract

For many scientists, researchers and students Markov chain Monte Carlo (MCMC) simulation is an important and necessary tool to perform Bayesian analyses. The simulation is often presented as a mathematical algorithm and then translated into an appropriate computer program. However, this can result in overlooking the fundamental and deeper conceptual ideas that are necessary for an effective diagnosis of MCMC output. In this paper we discuss MCMC simulation conceptually in the context of a Bayesian paradigm without revealing the formal algorithm first. We propose a tactile simulation method with a two-state discrete parameter where a coin supplies the proposal values and given the acceptance sets, the die value determines whether be not to accept the proposal.

Keywords:

• Markov chain Monte carlo
• simulation
• Bayesian inference
• Bayes’ box
• undergraduate teaching

Acknowledgments

Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/upri