Markov chain monte carlo methods: Theory and applications

Abstract

Markov chain Monte Carlo algorithms constitute flexible and powerful solutions to Bayesian inverse problems. They return a sample of the unapproximated posterior probability density, and make no assumptions as to linearity or the form of the prior or likelihood. MCMC algorithms are in principle easy to construct, however, they can prove difficult to implement in practice. This chapter describes the theory that underlies MCMC simulation, provides guidance for its practical implementation, and presents examples of applications of MCMC to satellite retrievals and model uncertainty characterization. Though the high dimensionality of Earth system datasets and the complexity of atmospheric, oceanic, and hydrologic models present significant challenges, continued advances in theory and practice are making application of MCMC algorithms increasingly feasible.