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.Case 1: b 0 5 1.1*b, s b0 5 0.1*b 0 ; Case 2: b 0 5 1.5*b, s b0 5 b 0 ; Case 3: b 0 5 10*b, s b0 5 0.1*b 0 . r 1 CCW corresponds to the first approach and r 2 CCW corresponds to the second approach for parameter ranking and selection when FIM is not invertible.Case 1: b 0 5 1.1*b, s b0 5 0.1*b 0 ; Case 2: b 0 5 1.5*b, s b0 5 b 0 ; Case 3: b 0 5 10*b, s b0 5 0.1*b 0 . r 1 CCW corresponds to the first approach and r 2 CCW corresponds to the second approach for parameter ranking and selection when FIM is not invertible. SM0 contains three parameters b 1 , b 2 , and b 3 and was selected using the r CC approach. SM1 contains two parameters b 1 and b 2 and was selected using the r 1 CCW approach. SM2 contains two parameters b 5 and b 6 and was selected using the r 2 CCW approach. The EM contains all seven parameters.

Sequential model-based A- and V-optimal design of experiments for building fundamental models of pharmaceutical production processes

“…Kravaris et al, 2013;Wu et al, 2008), pseudoinverse methods, e.g. (Eghtesadi and McAuley, 2016;Greville, 1959;Li and Yeh, 2012), Tikhonov regularization, e.g. (Hoerl and Kennard, 1970;Johansen, 1997;Tibshirani, 2011;Tikhonov et al, 1978) and Bayesian approaches, e.g.…”

Diagnosing Parameter Estimability Problems in Polymerization Models

“…Typical causes of estimability problems include: insensitivity of model predictions to changes in some of the less‐important parameters, correlated effects of parameter values on model predictions, and lack of information in the data. [ 5–8 ] To cope with these problems, modelers sometimes perform parameter estimability studies and then choose to estimate a subset of the model parameters, while fixing unestimable parameters at literature or nominal values. [5,8–16 ]…”

Reduced Hessian based parameter selection and estimation with simultaneous collocation approach

“…The MSE based approach was extended by using the orthogonalization algorithm to determine and fix the relatively unimportant parameters and then make the reduced FIM invertible, or by using the pseudo-inverse instead of the inverse of FIM. 18 The MSE based approaches 13,15,17,18 have to perform the weighted nonlinear least squares regression at each step. On the one hand, the total computation cost becomes heavy as the number of the estimated parameters increases.…”