Water Science and Engineering 2018, 11(2) 89-100 DOI:   https://doi.org/10.1016/j.wse.2018.06.001  ISSN: 1674-2370 CN: 32-1785/TV

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Keywords
Marginal likelihood
Posterior model probability
Advection-dispersion equation
Mobile-immobile model
Groundwater model
Authors
Saeideh Samani
Ming Ye
Fan Zhang
Yong-zhen Pei
Guo-ping Tang
Ahmed Elshall
Asghar A. Moghaddam
PubMed
Article by Saeideh Samani
Article by Ming Ye
Article by Fan Zhang
Article by Yong-zhen Pei
Article by Guo-ping Tang
Article by Ahmed Elshall
Article by Asghar A. Moghaddam

Impacts of prior parameter distributions on Bayesian evaluation of groundwater model complexity

Saeideh Samani a, b, Ming Ye b, c, d, *, Fan Zhang e, Yong-zhen Pei c, Guo-ping Tang f, Ahmed Elshall b, Asghar A. Moghaddam a

a Department of Earth Sciences, University of Tabriz, Tabriz 5166616471, Iran
b Department of Scientific Computing, Florida State University, Tallahassee FL 32306, USA
c School of Computer Science and Software Engineering, Tianjin Polytechnic University, Tianjin 300387, China
d Department of Earth, Ocean and Atmospheric Science, Florida State University, Tallahassee FL 32306, USA
e Key Laboratory of Tibetan Environment Changes and Land Surface Processes, Institute of Tibetan Plateau Research, Chinese Academy of Sciences, Beijing 100101, China
f Environmental Sciences Division, Oak Ridge National Laboratory, Oak Ridge TN 37831, USA

Abstract

This study used the marginal likelihood and Bayesian posterior model probability for evaluation of model complexity in order to avoid using over-complex models for numerical simulations. It focused on investigation of the impacts of prior parameter distributions (involved in calculating the marginal likelihood) on the evaluation of model complexity. We argue that prior parameter distributions should define the parameter space in which numerical simulations are made. New perspectives on the prior parameter distribution and posterior model probability were demonstrated in an example of groundwater solute transport modeling with four models, each simulating four column experiments. The models had different levels of complexity in terms of their model structures and numbers of calibrated parameters. The posterior model probability was evaluated for four cases with different prior parameter distributions. While the distributions substantially impacted model ranking, the model ranking in each case was reasonable for the specific circumstances in which numerical simulations were made. For evaluation of model complexity, it is thus necessary to determine the parameter spaces for modeling, which can be done by conducting numerical simulation and using engineering judgment based on understanding of the system being studied.

Keywords Marginal likelihood   Posterior model probability   Advection-dispersion equation   Mobile-immobile model   Groundwater model  
Received 2017-09-14 Revised 2018-01-10 Online: 2018-04-30 
DOI: https://doi.org/10.1016/j.wse.2018.06.001
Fund:

This work was supported by the U.S. Department of Energy Early Career Research Program Award (Grant No. DE-SC0008272) and U.S. National Science Foundation (Grant No. 1552329).

Corresponding Authors: Ming Ye
Email: mye@fsu.edu
About author:

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