Bayesian model order selection for nonlinear system function expansions.
Orthonormal function expansions have been used extensively in the context of linear and nonlinear systems identification, since they result in a significant reduction in the number of required free parameters. In particular, Laguerre basis expansions of Volterra kernels have been used successfully for physiological systems identification, due to the exponential decaying characteristics of the Laguerre orthonormal basis and the inherent nonlinearities that characterize such systems. A critical aspect of the Laguerre expansion technique is the selection of the model structural parameters, i.e., polynomial model order, number of Laguerre functions in the expansion and value of the Laguerre parameter alpha, which determines the rate of exponential decay. This selection is typically made by trial-and-error procedures on the basis of the model prediction error. In the present paper, we formulate the Laguerre expansion technique in a Bayesian framework and derive analytically the posterior distribution of the alpha parameter, as well as the model evidence, in order to infer on the expansion structural parameters. We also demonstrate the performance of the proposed method by simulated examples and compare it to alternative statistical criteria for model order selection.
Mitsis
Georgios D
GD
Department of Electrical and Computer Engineering, National Technical University of Athens, Zografou 15780, Greece. gmitsis@esd.ntua.gr
Jbabdi
Saad
S
D000465:Algorithms; D001499:Bayes Theorem; D003198:Computer Simulation; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D013598:Systems Theory