Jensen Anders Chr, Ditlevsen Susanne, Kessler Mathieu, Papaspiliopoulos Omiros
Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Oct;86(4 Pt 1):041114. doi: 10.1103/PhysRevE.86.041114. Epub 2012 Oct 10.
Excitability is observed in a variety of natural systems, such as neuronal dynamics, cardiovascular tissues, or climate dynamics. The stochastic FitzHugh-Nagumo model is a prominent example representing an excitable system. To validate the practical use of a model, the first step is to estimate model parameters from experimental data. This is not an easy task because of the inherent nonlinearity necessary to produce the excitable dynamics, and because the two coordinates of the model are moving on different time scales. Here we propose a Bayesian framework for parameter estimation, which can handle multidimensional nonlinear diffusions with large time scale separation. The estimation method is illustrated on simulated data.
兴奋性在多种自然系统中都有体现，比如神经元动力学、心血管组织或气候动力学。随机菲茨休 - 纳古莫模型就是一个代表可兴奋系统的突出例子。为了验证模型的实际用途，第一步是根据实验数据估计模型参数。这并非易事，一方面是因为产生可兴奋动力学所需的内在非线性，另一方面是因为模型的两个坐标在不同的时间尺度上变化。在此，我们提出一种用于参数估计的贝叶斯框架，它能够处理具有大时间尺度分离的多维非线性扩散。我们在模拟数据上展示了这种估计方法。
