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Exact Scheffé‐type confidence intervals for output from groundwater flow models: 2. Combined use of hydrogeologic information and calibration data
Author(s) -
Cooley Richard L.
Publication year - 1993
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/92wr01864
Subject(s) - confidence distribution , cdf based nonparametric confidence interval , confidence interval , credible interval , statistics , robust confidence intervals , mathematics , calibration , prior probability , confidence region , variance (accounting) , bayesian probability , accounting , business
Calibration data (observed values corresponding to model‐computed values of dependent variables) are incorporated into a general method of computing exact Scheffé‐type confidence intervals analogous to the confidence intervals developed in part 1 (Cooley, this issue) for a function of parameters derived from a groundwater flow model. Parameter uncertainty is specified by a distribution of parameters conditioned on the calibration data. This distribution was obtained as a posterior distribution by applying Bayes' theorem to the hydrogeologically derived prior distribution of parameters from part 1 and a distribution of differences between the calibration data and corresponding model‐computed dependent variables. Tests show that the new confidence intervals can be much smaller than the intervals of part 1 because the prior parameter variance‐covariance structure is altered so that combinations of parameters that give poor model fit to the data are unlikely. The confidence intervals of part 1 and the new confidence intervals can be effectively employed in a sequential method of model construction whereby new information is used to reduce confidence interval widths at each stage.