The dendritic spines play a crucial role in learning and memory processes, epileptogenesis, drug addiction, and postinjury recovery. The shape of the dendritic spine is a morphological key to understand learning and memory process. The classification of the dendritic spines is based on their shapes but the major questions are how the shapes changes in time, how the synaptic strength changes, and is there a correlation between shapes and synaptic strength? Because the changes of the classes by dendritic spines during activation are time dependent, the forward-directed autoregressive hidden Markov model (ARHMM) can be used to model these changes. It is also more appropriate to use an ARHMM directed backward in time. Thus, the mixture of forward-directed ARHMM and backward-directed ARHMM (MARHMM) is used to model time-dependent data related to the dendritic spines. In this article, we discuss (1) how to choose the initial probability vector and transition and dependence matrices in ARHMM and MARHMM for modeling the dendritic spines changes and (2) how to estimate these matrices. Many descriptors to classify dendritic spines in two-dimensional or/and three-dimensional (3D) are available. Our results from sensitivity analysis show that the classification that comes from 3D descriptors is closer to the truth, and estimated transition and dependence probability matrices are connected with the molecular mechanism of the dendritic spines activation.

中文翻译：

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激活过程中树突棘形态的自回归隐马尔可夫模型的混合。

树突棘在学习和记忆过程、癫痫发生、毒瘾和伤后恢复中起着至关重要的作用。树突棘的形状是理解学习和记忆过程的形态学关键。树突棘的分类是基于它们的形状，但主要问题是形状如何随时间变化，突触强度如何变化，形状与突触强度之间是否存在相关性？由于激活期间树突棘的类别变化是时间相关的，因此可以使用前向自回归隐马尔可夫模型 (ARHMM) 对这些变化进行建模。使用时间向后的 ARHMM 也更合适。因此，前向 ARHMM 和后向 ARHMM (MARHMM) 的混合用于模拟与树突棘相关的时间相关数据。在本文中，我们将讨论 (1) 如何在 ARHMM 和 MARHMM 中选择初始概率向量以及转移和依赖矩阵来对树突棘变化进行建模，以及 (2) 如何估计这些矩阵。许多描述符可以在二维或/和三维 (3D) 中对树突棘进行分类。我们的敏感性分析结果表明，来自 3D 描述符的分类更接近真实，并且估计的转移和依赖概率矩阵与树突棘激活的分子机制有关。我们讨论（1）如何在 ARHMM 和 MARHMM 中选择初始概率向量以及转移和依赖矩阵来对树突棘变化进行建模，以及（2）如何估计这些矩阵。许多描述符可以在二维或/和三维 (3D) 中对树突棘进行分类。我们的敏感性分析结果表明，来自 3D 描述符的分类更接近真实，并且估计的转移和依赖概率矩阵与树突棘激活的分子机制有关。我们讨论（1）如何在 ARHMM 和 MARHMM 中选择初始概率向量以及转移和依赖矩阵来对树突棘变化进行建模，以及（2）如何估计这些矩阵。许多描述符可以在二维或/和三维 (3D) 中对树突棘进行分类。我们的敏感性分析结果表明，来自 3D 描述符的分类更接近真实，并且估计的转移和依赖概率矩阵与树突棘激活的分子机制有关。