论文标题
贝叶斯近似与隐藏的半马尔科夫模型进行远程测量监测的体育锻炼
Bayesian Approximations to Hidden Semi-Markov Models for Telemetric Monitoring of Physical Activity
论文作者
论文摘要
我们提出了一个贝叶斯隐藏的马尔可夫模型，用于分析时间序列和顺序数据，其中将过渡概率矩阵的特殊结构嵌入到模型中，以模拟显式 - 持续性半马克维亚动力学。我们的配方允许开发高度灵活和可解释的模型，这些模型可以在状态持续时间内整合可用的先前信息，同时保持中等的计算成本以执行有效的后验推断。在模型选择和样本外预测方面，我们展示了选择一种贝叶斯估计方法的贝叶斯方法的好处，同时也强调了我们推理程序的计算可行性，同时导致可忽略不计的统计误差。在与电子健康相关的应用中说明了我们的方法论的使用，在该应用程序中，我们使用通过可穿戴感应装置收集的远程测光活动数据研究了静止性节奏。该分析首次考虑了贝叶斯模型选择显式状态停留分布的形式。我们进一步研究了将昼夜节律协变量纳入发射密度，并以数据驱动的方式估算了这一点。
We propose a Bayesian hidden Markov model for analyzing time series and sequential data where a special structure of the transition probability matrix is embedded to model explicit-duration semi-Markovian dynamics. Our formulation allows for the development of highly flexible and interpretable models that can integrate available prior information on state durations while keeping a moderate computational cost to perform efficient posterior inference. We show the benefits of choosing a Bayesian approach for HSMM estimation over its frequentist counterpart, in terms of model selection and out-of-sample forecasting, also highlighting the computational feasibility of our inference procedure whilst incurring negligible statistical error. The use of our methodology is illustrated in an application relevant to e-Health, where we investigate rest-activity rhythms using telemetric activity data collected via a wearable sensing device. This analysis considers for the first time Bayesian model selection for the form of the explicit state dwell distribution. We further investigate the inclusion of a circadian covariate into the emission density and estimate this in a data-driven manner.
