Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4525504 | Advances in Water Resources | 2015 | 10 Pages |
Abstract
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 the log-transmissivity field of the medium is inferred from scarce and noisy data. For this purpose, the stochastic field is expanded onto a set of orthogonal functions using a Karhunen-Loève (KL) transformation. Though the prior guess on the stochastic structure (covariance) of the transmissivity field is erroneous, the MCPD inference of the KL coefficients is able to extract relevant inverse solutions.
Keywords
Related Topics
Physical Sciences and Engineering
Earth and Planetary Sciences
Earth-Surface Processes
Authors
Thierry A. Mara, Noura Fajraoui, Anis Younes, Frederick Delay,