The Shark Attack Problem Revisited: MCMC with the Metropolis Algorithm

In this chapter, the “Shark Attack Problem” (Chapter 11) is revisited. Markov Chain Monte Carlo (MCMC) is introduced as another way to determine a posterior distribution of λ‎, the mean number of shark attacks per year. The MCMC approach is so versatile that it can be used to solve almost any kind of parameter estimation problem. The chapter highlights the Metropolis algorithm in detail and illustrates its application, step by step, for the “Shark Attack Problem.” The posterior distribution generated in Chapter 11 using the gamma-Poisson conjugate is compared with the MCMC posterior distribution to show how successful the MCMC method can be. By the end of the chapter, the reader should also understand the following concepts: tuning parameter, MCMC inference, traceplot, and moment matching.