Discipline: Mathematics & Statistics
Subcategory: STEM Research
Arunasalam Rahunanthan - Central State University
Co-Author(s): Abdullah Al-Mamun, University of Texas at Dallas; Felipe Pereira, University of Texas at Dallas
We consider the prediction of contaminant in a water aquifer. In order to predict the contaminant concentration in time, we first characterize the subsurface properties of the aquifer, such as permeability, by using very limited data in the form of fractional flow curves in monitoring wells of the aquifer. A Bayesian statistical framework is used for reconstructing the permeability distribution of the aquifer. In the framework we run several parallel Markov Chain Monte Carlo (MCMC) simulations. In this approach, we need to determine when it is safe to stop the MCMC simulations for a reliable characterization of the permeability field. There are several convergence diagnostics available for this purpose and those diagnostics fall into two categories: the first category of diagnostics entirely depends on the output values of the MCMC simulation and those in the second category use not only the output values but also the information on the target distribution. In the first category, Brooks and Gelman  proposed a convergence diagnostic that uses Multivariate Potential Scale Reduction Factor (MPSRF) to decide when to terminate MCMC simulations. In this poster presentation, we first propose a fitting procedure for the MPRSF data that allows us to estimate the number of iterations for the convergence. Then we present an analysis of ensembles of fractional flow curves suggesting that the number of iterations required for convergence through the MPSRF analysis is excessive. Also, the analysis, which is our proposed convergence diagnostic, provides a criterion to stop MCMC simulations for a reliable prediction of the contaminant in the aquifer. The prediction results indicate that the proposed convergence diagnostic is very reliable in our application. Reference:  A. Gelman and S. Brooks, General methods for monitoring convergence of iterative simulations, Journal of Computational and Graphical Statistics, vol. 7, pp. 434–455, 1998.
Funder Acknowledgement(s): HRD-1600818
Faculty Advisor: None Listed,
NSF Affiliation: HBCU-UP