基于贝叶斯样条的隐马尔可夫模型及其在活动测量数据和睡眠分析中的应用
Bayesian spline-based hidden Markov models with applications to actimetry data and sleep analysis
AI总结：
本文提出基于 B-spline 发射分布的贝叶斯 HMM 框架，利用跨维 MCMC 与边际似然同时估计结点配置和状态数，并通过模拟、鲨鱼活动及人类睡眠昼夜节律分析验证其灵活性与优势。
摘要：
基于 B-spline 的隐马尔可夫模型利用 B-spline 来设定发射分布，相比传统参数化 HMM，为数据提供了一种更灵活的建模方法。我们引入了一个用于推断的贝叶斯框架，能够同时估计包括状态数在内的所有未知模型参数。通过使用跨维马尔可夫链抽样算法，可以识别 B-spline 的简约结点配置；而关于状态数的模型选择，则可在并行抽样框架内基于边际似然进行。通过大量模拟研究，我们证明了该方法相对于替代方法的优越性，以及其稳健性和可扩展性。我们通过动物活动数据（即白鳍鲨数据）展示了该方法的探索性用途。我们的贝叶斯方法的灵活性还有助于纳入更现实的假设；为此，我们开发了一种新颖的分层条件 HMM，用于分析人类活动，以进行昼夜节律和睡眠建模。
英文摘要：
B-spline-based hidden Markov models employ B-splines to specify the emission distributions, offering a more flexible modelling approach to data than conventional parametric HMMs. We introduce a Bayesian framework for inference, enabling the simultaneous estimation of all unknown model parameters including the number of states. A parsimonious knot configuration of the B-splines is identified by the use of a trans-dimensional Markov chain sampling algorithm, while model selection regarding the number of states can be performed based on the marginal likelihood within a parallel sampling framework. Using extensive simulation studies, we demonstrate the superiority of our methodology over alternative approaches as well as its robustness and scalability. We illustrate the explorative use of our methods for data on activity in animals, i.e. whitetip-sharks. The flexibility of our Bayesian approach also facilitates the incorporation of more realistic assumptions and we demonstrate this by developing a novel hierarchical conditional HMM to analyse human activity for circadian and sleep modelling.
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