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CALCULATION OF NONLINEAR CONFIDENCE AND PREDICTION INTERVALS FOR GROUND‐WATER FLOW MODELS 1
Author(s) -
Cooley Richard L.,
Vecchia Aldo V.
Publication year - 1987
Publication title -
jawra journal of the american water resources association
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.957
H-Index - 105
eISSN - 1752-1688
pISSN - 1093-474X
DOI - 10.1111/j.1752-1688.1987.tb00834.x
Subject(s) - quantile , confidence interval , range (aeronautics) , nonlinear system , confidence and prediction bands , random variable , monte carlo method , prediction interval , statistics , mathematics , engineering , physics , quantum mechanics , aerospace engineering
ABSTRACT: A method is derived to efficiently compute nonlinear confidence and prediction intervals on any function of parameters derived as output from a mathematical model of a physical system. The method is applied to the problem of obtaining confidence and prediction intervals for manually‐calibrated ground‐water flow models. To obtain confidence and prediction intervals resulting from uncertainties in parameters, the calibrated model and information on extreme ranges and ordering of the model parameters within one or more independent groups are required. If random errors in the dependent variable are present in addition to uncertainties in parameters, then calculation of prediction intervals also requires information on the extreme range of error expected. A simple Monte Carlo method is used to compute the quantiles necessary to establish probability levels for the confidence and prediction intervals. Application of the method to a hypothetical example showed that includsion of random errors in the dependent variable in addition to uncertainties in parameters can considerably widen the prediction intervals.