ABSTRACT
This chapter discusses a Markov Chain Monte Carlo (MCMC) sample by constructing a time series in which an accept-reject algorithm governs its dynamics. It presents a general form of MCMC as Metropolis-Hastings (M-H) and shows how to arrive at special cases of M-H, resulting in the well-known Gibbs sampler, among others. The M-H ratio acts as a criterion for accepting or rejecting the proposed value based on how well it suits the likelihood and prior. Another important aspect to consider in the MCMC algorithm when M-H updates are used is the proposal. MCMC is a stochastic sampling method like MC, but is Markov because it results in dependent samples rather than independent samples. Autocorrelation in MCMC samples can affect the precision associated with MC integration and therefore the inference that is made based on these methods for fitting statistical models to data.
