聚合马尔可夫过程的最大似然估计
Maximum likelihood estimation of aggregated Markov processes.
作者信息
Qin F, Auerbach A, Sachs F
机构信息
Department of Biophysical Sciences, State University of New York at Buffalo 14214, USA.
出版信息
Proc Biol Sci. 1997 Mar 22;264(1380):375-83. doi: 10.1098/rspb.1997.0054.
Abstract
We present a maximum likelihood method for the modelling of aggregated Markov processes. The method utilizes the joint probability density of the observed dwell time sequence as likelihood. A forward-backward recursive procedure is developed for efficient computation of the likelihood function and its derivatives with respect to the model parameters. Based on the calculated forward and backward vectors, analytical formulae for the derivatives of the likelihood function are derived. The method exploits the variable metric optimizer for search of the likelihood space. It converges rapidly and is numerically stable. Numerical examples are given to show the effectiveness of the method.
摘要
我们提出了一种用于聚合马尔可夫过程建模的最大似然方法。该方法利用观测到的驻留时间序列的联合概率密度作为似然函数。开发了一种前向-后向递归过程，用于高效计算似然函数及其关于模型参数的导数。基于计算出的前向和后向向量，推导了似然函数导数的解析公式。该方法利用变尺度优化器搜索似然空间。它收敛迅速且数值稳定。给出了数值例子以说明该方法的有效性。
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