Hidden Markov models (HMMs) have been applied in various domains, which makes the identifiability issue of HMMs popular among researchers. Classical identifiability conditions shown in previous studies are too strong for practical analysis. In this paper, we propose generic identifiability conditions for discrete time HMMs with finite state space. Also, recent studies about cognitive diagnosis models (CDMs) applied first-order HMMs to track changes in attributes related to learning. However, the application of CDMs requires a known \(\varvec{Q}\) matrix to infer the underlying structure between latent attributes and items, and the identifiability constraints of the model parameters should also be specified. We propose generic identifiability constraints for our restricted HMM and then estimate the model parameters, including the \(\varvec{Q}\) matrix, through a Bayesian framework. We present Monte Carlo simulation results to support our conclusion and apply the developed model to a real dataset.

隐马尔可夫模型（HMMs）已被应用到各个领域，这使得HMMs的可识别性问题受到研究人员的青睐。先前研究中显示的经典可识别性条件对于实际分析来说太强了。在本文中，我们提出了具有有限状态空间的离散时间 HMM 的通用可识别性条件。此外，最近关于认知诊断模型 (CDM) 的研究应用一阶 HMM 来跟踪与学习相关的属性变化。但是，CDM 的应用需要一个已知的\(\varvec{Q}\)矩阵来推断潜在属性和项目之间的底层结构，并且还应该指定模型参数的可识别性约束。我们为我们的受限 HMM 提出了通用的可识别性约束，然后通过贝叶斯框架估计模型参数，包括\(\varvec{Q}\)矩阵。我们提供蒙特卡罗模拟结果来支持我们的结论，并将开发的模型应用于真实数据集。