Bayesian methods in hydrologic modeling: A study of recent advancements in Markov chain Monte Carlo techniques

Bayesian methods, and particularly Markov chain Monte Carlo (MCMC) techniques, are extremely useful in uncertainty assessment and parameter estimation of hydrologic models. However, MCMC algorithms can be difficult to implement successfully because of the sensitivity of an algorithm to model initialization and complexity of the parameter space. Many hydrologic studies, even relatively simple conceptualizations, are hindered by complex parameter interactions where typical uncertainty methods are harder to apply. This paper presents comparisons between three recently introduced MCMC approaches, the adaptive Metropolis, the delayed rejection adaptive Metropolis, and the differential evolution Markov chain algorithms via two case studies: (1) a synthetic Gaussian mixture with five parameters and two modes and (2) a real‐world hydrologic modeling scenario where each algorithm will serve as the uncertainty and parameter estimation framework for a conceptual precipitation‐runoff model.