STANDARD ERRORS AND CONFIDENCE-INTERVALS IN NONLINEAR-REGRESSION - COMPARISON OF MONTE-CARLO AND PARAMETRIC STATISTICS

A Monte Carlo method is employed to characterize distributions of parameter values calculated in nonlinear regression problems. Accurate estimates of confidence intervals are easily obtained. Two illustrative numerical examples are provided to compare the Monte Carlo uncertainty estimates with those derived by use of standard methods of parametric statistics. The customary assumptions that (1) the effects of covariances between pairs of the parameters can be ignored and (2) that the distributions of the parameters are normal are shown to lead to significant errors, up to 2- and 3-fold in the calculated uncertainties. The Monte Carlo method is free from these assumptions and their associated errors. © 1990 American Chemical Society.