Comparison of Parameter Estimation Design Criteria Using a Solute Transport Model with Matrix Diffusion

Abstract

Three criteria for the experimental design of parameter estimation are compared by using the criteria to develop sampling patterns for determining parameter values in one‐dimensional transport models. The models include advection, dispersion, and matrix diffusion, the latter being an important process for nuclear waste isolation. The effectiveness of various designs is assessed by studying expected errors of parameter estimates and correlation between parameters. The correlations and expected errors are computed using parameter sensitivities, and the results demonstrate that the choice of design criterion can make a significant difference in the expected estimation error of parameter values in sparse designs. The best overall choice is D‐optimality, which is a measure of the volume of the joint confidence ellipsoid of the parameter estimates. E‐optimality, which minimizes the longest axis of the confidence ellipsoid, gives somewhat similar results but is not as robust for all of the estimated parameters. It is also shown that approaches that consider parameter sensitivities, but not correlation between parameters, may result in inferior designs.

An adaptive Gaussian process‐based method for efficient Bayesian experimental design in groundwater contaminant source identification problems

“…The solution criteria are usually derived from the covariance matrix of the parameters, including the well‐known “alphabetic optimality” conditions [ Atkinson et al ., ; Chaloner and Verdinelli , ]. In the experimental design for parameter estimation of groundwater models, A‐optimality [minimization of the trace of the covariance matrix, e.g., Hsu and Yeh , ], D‐optimality [minimization of the determinant of the covariance matrix, e.g., Catania and Paladino , ] and E‐optimality [minimization of the eigenvalue of the covariance matrix, e.g., Nordqvist, ] are most commonly used. To figure out which design criterion has the best overall performance, Nordqvist [] and Sciortino et al .…”

Model-data interaction in groundwater studies: Review of methods, applications and future directions

“…al., 2000;Peng et al, 2011;Zhou et al, 2014). However, groundwater MDI has several specific characteristics that affect the choice of a synthesis method: (1) groundwater models are moderately to highly nonlinear (Samuel and Jha, 2003;Schöniger et al, 2012;Wallis et al, 2014;Siade et al, 2017), (2) they result in state variables (e.g.…”

“…Catania and Paladino, 2009;Siade et al, 2017), E-optimality (minimizing the eigenvalue of the covariance matrix, e.g. Nordqvist, 2000), or expected Shannon information gain (i.e. relative entropy, e.g.…”