Inversion and uncertainty of highly parameterized models in a Bayesian framework by sampling the maximal conditional posterior distribution of parameters

We introduce the concept of Maximal Conditional Posterior Distribution (MCPD) to assess the uncertainty of model parameters in a Bayesian framework. Although, Markov Chains Monte Carlo (MCMC) methods are particularly suited for this task, they become challenging with highly parameterized nonlinear models. The MCPD represents the conditional probability distribution function of a given parameter knowing that the other parameters maximize the conditional posterior density function. Unlike MCMC which accepts or rejects solutions sampled in the parameter space, MCPD is calculated through several optimization processes. Model inversion using MCPD algorithm is particularly useful for highly parameterized problems because calculations are independent. Consequently, they can be evaluated simultaneously with a multi-core computer. In the present work, the MCPD approach is applied to invert a 2D stochastic groundwater flow problem where ∗Corresponding author: [email protected] ∗Published in Advances in Water Resources, Vol. 76, pp. 1-10, 2014, doi:10.1016/j.advwatres.2014.11.013