Sensitivity analysis of kernel estimates: implications in nonlinear physiological system identification

Abstract

Many techniques have been developed for the estimation of the Volterra/Wiener kernels of nonlinear systems, and have found extensive application in the study of various physiological systems. To date, however, we are not aware of methods for estimating the reliability of these kernels from single data records. In this study, we develop a formal analysis of variance for least-squares based nonlinear system identification algorithms. Expressions are developed for the variance of the estimated kernel coefficients and are used to place confidence bounds around both kernel estimates and output predictions. Specific bounds are developed for two such identification algorithms: Korenberg's fast orthogonal algorithm and the Laguerre expansion technique. Simulations, employing a model representative of the peripheral auditory system, are used to validate the theoretical derivations, and to explore their sensitivity to assumptions regarding the system and data. The simulations show excellent agreement between the variances of kernel coefficients and output predictions as estimated from the results of a single trial compared to the same quantities computed from an ensemble of 1000 Monte Carlo runs. These techniques were validated with white and nonwhite Gaussian inputs and with white Gaussian and nonwhite non-Gaussian measurement noise on the output, provided that the output noise source was independent of the test input.