Jump Box–Jenkins (BJ) models are a collection of a finite set of linear dynamical submodels in BJ form that switch over time, according to a Markov chain. This paper addresses the problem of maximum-a-posteriori estimation of jump BJ models from a given training input/output dataset. The proposed solution method estimates the coefficients of the BJ submodels, the state transition probabilities of the Markov chain regulating the switching of operating modes, and the corresponding mode sequence hidden in the dataset. In particular, the posterior distribution of all the unknown variables characterizing the jump BJ model is derived and then maximized using a coordinate ascent algorithm. The resulting estimation algorithm alternates between Gauss–Newton optimization of the coefficients of the BJ submodels, a method derived based on an instance of prediction error methods tailored to BJ models with switching coefficients, and approximated dynamic programming for optimization of the sequence of active modes. The quality of the proposed estimation approach is evaluated on a numerical example based on synthetic data and in a case study related to segmentation of honeybee dances.

跳转箱詹金斯（BJ）模型在BJ形式的有限组线性动态子模型的集合，开关随着时间的推移，根据一个Markov链。本文讨论了最大后验问题从给定的训练输入/输出数据集中估计跳跃BJ模型。所提出的求解方法估计BJ子模型的系数，调节操作模式切换的马尔可夫链的状态转移概率，以及隐藏在数据集中的相应模式序列。特别是，导出了表征跳跃BJ模型的所有未知变量的后验分布，然后使用坐标上升算法将其最大化。结果估计算法在BJ子模型的系数的高斯-牛顿优化之间交替，这是一种基于预测误差方法实例的方法针对具有开关系数的BJ模型进行量身定制，并采用近似动态编程来优化活动模式的顺序。在基于合成数据的数值示例以及与蜜蜂舞蹈分割相关的案例研究中，对所提出的估计方法的质量进行了评估。