Hidden Markov models (HMMs) are probabilistic methods in which observations are seen as realizations of a latent Markov process with discrete states that switch over time. Moving beyond standard statistical tests, HMMs offer a statistical environment to optimally exploit the information present in multivariate time series, uncovering the latent dynamics that rule them. Here, we extend the Poisson HMM to the multilevel framework, accommodating variability between individuals with continuously distributed individual random effects following a lognormal distribution, and describe how to estimate the model in a fully parametric Bayesian framework. The proposed multilevel HMM enables probabilistic decoding of hidden state sequences from multivariate count time-series based on individual-specific parameters, and offers a framework to quantificate between-individual variability formally. Through a Monte Carlo study we show that the multilevel HMM outperforms the HMM for scenarios involving heterogeneity between individuals, demonstrating improved decoding accuracy and estimation performance of parameters of the emission distribution, and performs equally well when not between heterogeneity is present. Finally, we illustrate how to use our model to explore the latent dynamics governing complex multivariate count data in an empirical application concerning pilot whale diving behaviour in the wild, and how to identify neural states from multi-electrode recordings of motor neural cortex activity in a macaque monkey in an experimental set up. We make the multilevel HMM introduced in this study publicly available in the R-package mHMMbayes in CRAN.

翻译：隐马尔可夫模型（HMM）是一种概率方法，其将观测值视为由离散状态随时间切换的潜在马尔可夫过程生成的实现。HMM超越了标准统计检验，提供了一种统计框架，能够最优地利用多元时间序列中的信息，揭示支配这些序列的潜在动态。本文在多层次框架中扩展了泊松HMM，通过服从对数正态分布的连续个体随机效应来容纳个体间的变异性，并描述了如何在完全参数化贝叶斯框架中估计该模型。所提出的多层次HMM能够基于个体特定参数从多元计数时间序列中对隐状态序列进行概率解码，并提供了一种正式量化个体间变异性的框架。通过蒙特卡洛研究，我们证明多层次HMM在个体间存在异质性的场景中优于标准HMM，展现了更优的解码准确性和发射分布参数的估计性能；当不存在个体间异质性时，其表现同样优异。最后，我们通过两个实证案例展示了模型的应用：一是利用该模型探索野生领航鲸潜水行为中控制复杂多元计数数据的潜在动态；二是在实验设置中，从猕猴运动神经皮层活动的多电极记录中识别神经状态。本研究所引入的多层次HMM已在CRAN的R包mHMMbayes中公开提供。