The White House Problem Revisited: MCMC with the Metropolis–Hastings Algorithm

Abstract

The “White House Problem” of Chapter 10 is revisited in this chapter. Markov Chain Monte Carlo (MCMC) is used to build the posterior distribution of the unknown parameter p, the probability that a famous person could gain access to the White House without invitation. The chapter highlights the Metropolis–Hastings algorithm in MCMC analysis, describing the process step by step. The posterior distribution generated in Chapter 10 using the beta-binomial conjugate is compared with the MCMC posterior distribution to show how successful the MCMC method can be. By the end of this chapter, the reader will have a firm understanding of the following concepts: Monte Carlo, Markov chain, Metropolis–Hastings algorithm, Metropolis–Hastings random walk, and Metropolis–Hastings independence sampler.