Trendelkamp-Schroer Benjamin, Wu Hao, Paul Fabian, Noé Frank
Institut für Mathematik und Informatik, FU Berlin, Arnimallee 6, 14195 Berlin, Germany.
J Chem Phys. 2015 Nov 7;143(17):174101. doi: 10.1063/1.4934536.
Reversibility is a key concept in Markov models and master-equation models of molecular kinetics. The analysis and interpretation of the transition matrix encoding the kinetic properties of the model rely heavily on the reversibility property. The estimation of a reversible transition matrix from simulation data is, therefore, crucial to the successful application of the previously developed theory. In this work, we discuss methods for the maximum likelihood estimation of transition matrices from finite simulation data and present a new algorithm for the estimation if reversibility with respect to a given stationary vector is desired. We also develop new methods for the Bayesian posterior inference of reversible transition matrices with and without given stationary vector taking into account the need for a suitable prior distribution preserving the meta-stable features of the observed process during posterior inference. All algorithms here are implemented in the PyEMMA software--http://pyemma.org--as of version 2.0.
可逆性是马尔可夫模型和分子动力学主方程模型中的一个关键概念。对编码模型动力学性质的转移矩阵进行分析和解释，在很大程度上依赖于可逆性性质。因此，从模拟数据估计可逆转移矩阵对于先前发展理论的成功应用至关重要。在这项工作中，我们讨论了从有限模拟数据中进行转移矩阵最大似然估计的方法，并提出了一种新算法，用于在需要关于给定平稳向量的可逆性估计时进行估计。我们还开发了新方法，用于在考虑后验推断期间需要合适的先验分布以保留观察过程的亚稳态特征的情况下，对有和没有给定平稳向量的可逆转移矩阵进行贝叶斯后验推断。这里所有的算法都在PyEMMA软件（http://pyemma.org）中实现，版本为2.0 。
