A comparison of two Bayesian approaches for uncertainty quantification

Statistical calibration of model parameters conditioned on observations is performed in a Bayesian framework by evaluating the joint posterior probability density function (pdf) of the parameters. The posterior pdf is very often inferred by sampling the parameters with Markov Chain Monte Carlo (MCMC) algorithms. Recently, an alternative technique to calculate the so-called Maximal Conditional Posterior Distribution (MCPD) appeared. This technique infers the individual probability distribution of a given parameter under the condition that the other parameters of the model are optimal. Whereas the MCMC approach samples probable draws of the parameters, the MCPD samples the most probable draws when one of the parameters is set at various prescribed values. In this study, the results of a user-friendly MCMC sampler called DREAM(ZS) and those of the MCPD sampler are compared. The differences between the two approaches are highlighted before running a comparison inferring two analytical distributions with collinearity and multimodality. Then, the performances of both samplers are compared on an artificial multistep outflow experiment from which the soil hydraulic parameters are inferred. The results show that parameter and predictive uncertainties can be accurately assessed with both the MCMC and MCPD approaches.