In this article, mixed-effects state space models (MESSM, [Liu D, Lu T, Niu X-F, et al. Mixed-effects state-space models for analysis of longitudinal dynamic systems. Biometrics. 2011;67(2):476–485.]) are revisited. MESSM can be considered as an alternative to study the HIV dynamic in a longitudinal data environment, defining the mixed-effects component into state-space models setup. As in Liu et al.[Liu D, Lu T, Niu X-F, et al. Mixed-effects state-space models for analysis of longitudinal dynamic systems. Biometrics. 2011;67(2):476–485.], we consider a hierarchical structure to capture possible differences between the immune systems for different patients. We extend MESSM, allowing observational errors to follow a more flexible distribution to take account for heavy tails. Using the Bayesian paradigm, an efficient Markov Chain Monte Carlo (MCMC) algorithm based on McCausland et al. [McCausland WJ, Miller S, Pelletier D. Simulation smoothing for state.space models: A computational efficiency analysis. Comput Stat Data Anal. 2011;55(1):199–212.] is introduced for parameter and latent variables estimation. Moreover, the mixing variables obtained as a by-product of the scale mixture representation can be used to identify outliers. The methodology is illustrated using artificial and real datasets in order to investigate the properties and performance of the proposed model.

中文翻译：

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具有 Student-t 误差的混合效应状态空间模型

在本文中，混合效应状态空间模型（MESSM, [Liu D, Lu T, Niu XF, et al. Mixed-effects state-space models for analysis of Vertical dynamic systems. Biometrics. 2011;67(2):476 –485.]）被重新审视。MESSM 可被视为在纵向数据环境中研究 HIV 动态的替代方案，将混合效应组件定义为状态空间模型设置。如刘等人[Liu D, Lu T, Niu XF, et al. [Liu D, Lu T, Niu XF, et al. 用于纵向动态系统分析的混合效应状态空间模型。生物识别。2011;67(2):476-485.]，我们考虑了一个层次结构来捕捉不同患者免疫系统之间可能的差异。我们扩展了 MESSM，允许观测误差遵循更灵活的分布，以考虑重尾。使用贝叶斯范式，基于 McCausland 等人的高效马尔可夫链蒙特卡罗 (MCMC) 算法。[McCausland WJ、Miller S、Pelletier D. 状态空间模型的模拟平滑：计算效率分析。计算统计数据分析。2011;55(1):199–212.] 被引入参数和潜在变量估计。此外，作为尺度混合表示的副产品获得的混合变量可用于识别异常值。该方法使用人工和真实数据集进行说明，以研究所提出模型的属性和性能。作为比例混合表示的副产品获得的混合变量可用于识别异常值。该方法使用人工和真实数据集进行说明，以研究所提出模型的属性和性能。作为比例混合表示的副产品获得的混合变量可用于识别异常值。该方法使用人工和真实数据集进行说明，以研究所提出模型的属性和性能。