Handling non-negativity in deconvolution of physiological signals: a nonlinear stochastic approach.
A stochastic interpretation of Tikhonov regularization has been recently proposed to attack some open problems of deconvolution when dealing with physiological systems, i.e., in addition to ill-conditioning, infrequent and nonuniform sampling and necessity of having credible confidence intervals. However, the possible violation of the non-negativity constraint cannot be dealt with on firm statistical grounds, since the model of the unknown signal is compatible with negative realizations. In this paper, we propose a new model of the unknown input which excludes negative values. The model is embedded within a Bayesian estimation framework to calculate, by resorting to a Markov chain Monte Carlo algorithm, a nonlinear estimate of the unknown input given by its a posteriori expected value. Applications to simulated and real hormone secretion/pharmacokinetic problems are presented which show that this nonlinear approach is more accurate than the linear one. In addition, more realistic confidence intervals are obtained.
Pillonetto
Gianluigi
G
Dipartimento di Ingegneria dell'Informazione, Università degli Studi di Padova, Via Gradenigo 6a, 35131 Padova, Italy.
Sparacino
Giovanni
G
Cobelli
Claudio
C
D000465:Algorithms; D001499:Bayes Theorem; D003198:Computer Simulation; D007986:Luteinizing Hormone / Q000378:metabolism; D008390:Markov Chains; D008954:Models, Biological; D015233:Models, Statistical; D009010:Monte Carlo Method; D017711:Nonlinear Dynamics; D011786:Quality Control; D012044:Regression Analysis; D012680:Sensitivity and Specificity; D013223:Statistics as Topic / Q000379:methods*; D013269:Stochastic Processes
D007986:Luteinizing Hormone