Pillonetto Gianluigi, Sparacino Giovanni, Cobelli Claudio
Dipartimento di Ingegneria dell'Informazione, Università degli Studi di Padova, Via Gradenigo 6a, 35131 Padova, Italy.
Ann Biomed Eng. 2002 Sep;30(8):1077-87. doi: 10.1114/1.1510449.
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.
最近有人提出对蒂霍诺夫正则化进行随机解释，以解决处理生理系统时反卷积的一些开放性问题，即除了病态问题、采样不频繁和不均匀以及需要有可靠的置信区间之外的问题。然而，由于未知信号模型与负实值兼容，所以无法基于坚实的统计依据来处理可能违反非负性约束的情况。在本文中，我们提出了一种排除负值的未知输入新模型。该模型嵌入在贝叶斯估计框架中，通过马尔可夫链蒙特卡罗算法来计算未知输入的非线性估计值，该估计值由其后验期望值给出。文中给出了对模拟和实际激素分泌/药代动力学问题的应用，结果表明这种非线性方法比线性方法更准确。此外，还获得了更符合实际的置信区间。
