Mean‐squared‐error‐based method for parameter ranking and selection with noninvertible fisher information matrix

Abstract

Two approaches are developed to rank and select model parameters for estimation in complex models when data are limited, the Fisher information matrix (FIM) is noninvertible, and accurate predictions are desired at key operating conditions. These approaches are evaluated using synthetic data sets in a linear regression example to examine the influence of several factors including: the quality of initial parameter guesses, uncertainty ranges for initial parameter values, noise variances, and the operating region of interest. It is shown that using a reduced FIM with full rank leads to more reliable model predictions for a variety of cases than the alternative approach using the pseudoinverse of the FIM. The proposed reduced‐FIM methodology also provides better predictions than related techniques that do not consider the operating region where reliable predictions are required. The methodology is illustrated using a nonlinear differential equation model of a polymer film casting process. © 2015 American Institute of Chemical Engineers AIChE J, 62: 1112–1125, 2016