An explicit-duration Hidden Markov Model with a nonparametric kernel estimator of the state duration distribution is specified. The motivation comes from the physical problem of extracting the maximum information from an open quantum system subject to an external perturbation, which induces a change in the dynamics of the system. A nonparametric kernel estimator for discrete data is introduced, which is consistent and improves the estimates accuracy in presence of sparse data. To reconstruct the hidden dynamics, a Viterbi algorithm is used, which is robust against the underflow problem. Finite sample properties are investigated through an extensive Monte Carlo study showing that our formulation outperforms the original one both in small and in large samples.

指定了具有状态持续时间分布的非参数内核估计量的显式持续时间隐马尔可夫模型。动机来自物理问题，即从受外部扰动的开放量子系统中提取最大信息，从而引起系统动力学的变化。引入了用于离散数据的非参数核估计器，该估计器是一致的，并且在存在稀疏数据的情况下提高了估计精度。为了重建隐藏的动力学，使用了维特比算法，该算法对下溢问题具有鲁棒性。通过广泛的蒙特卡洛研究对有限样品的性能进行了研究，结果表明无论是大样品还是小样品，我们的配方均优于原始配方。