| Abstrakt: |
In this work, we study the robustness of nonlinear regression methods under uncertainty for parameter estimation for chemical kinetics models. We used Monte Carlo simulation to study the influence of two main types of uncertainty, namely, random errors and incomplete experimental data sets. The regression methods analyzed were least-squares minimization (LSM), maximum likelihood (ML), and a method that automatically reweights the objective function during the course of the optimization called IVEM (inside-variance estimation method). Although this work represents a preliminary attempt toward understanding the effects of uncertainty in nonlinear regression, the results from the analysis of the case studies indicate that the performance of the regression procedures can be highly sensitive to uncertainty due to random errors and incomplete data sets. The results also suggest that traditional methods of assigning weights a priori to regression functions can affect the performance of the regression unless these weights correspond to a careful characterization of the residual statistics of the regression problem. In the case in which there is no prior knowledge of these weights (particularly in maximum likelihood regression), we suggest that they be characterized, in a preliminary way, by performing a least-squares minimization regression first or by using a method that automatically estimates these weights during the course of the regression (IVEM). We believe that the performance of regression techniques under uncertainty requires attention before a regression method is chosen or the parameters obtained are deemed valid. |
