A COMPARISON OF ALGORITHMS FOR GLOBAL CHARACTERIZATION OF CONFIDENCE-REGIONS FOR NONLINEAR MODELS

Environmental models are often highly nonlinear, and parameters have t o be estimated from noisy data. The standard approach of locally linea rizing the model, which leads to ellipsoid confidence regions, is inap propriate in this situation. A straightforward technique to characteri ze arbitrary-shaped confidence regions is to calculate model output on a grid of parameter values. Each parameter value P results in a goodn ess of fit G(P), which allows delineation of the set of parameters cor responding to G(P) < G(c), with G(c) some threshold level(e.g., 5% pro bability). This approach is impractical and time-consuming for complex models, however. This article aims at finding an efficient alternativ e. It is first shown that the most general approach is to generate par ameter values uniformly covering the set G(P) < G(c) rather than findi ng the boundary G(P) = G(c). It is argued that the most efficient meth od of generating a uniform cover is by a (theoretical) algorithm known as pure adaptive search CPAS); the presently proposed method (uniform covering by probabilistic rejection; UCPR) is shown to be a good appr oximation to PAS, The UCPR is compared with alternative methods for a number of test problems. It is illustrated that for complex models (wh ere model run time dominates total computer time) UCPR is considerably faster and its cover of G(c) more uniform than existing alternatives. An intrinsic problem common to all methods is that the amount of work increases at least quadratically with the number of parameters consid ered, making them of limited use for high-dimensional problems.