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.

翻译：基于B样条的隐马尔可夫模型利用B样条拟合发射分布，相比传统参数化HMM提供了更灵活的数据建模方法。我们引入贝叶斯推断框架，能够同时估计包括状态数量在内的所有未知模型参数。通过跨维度马尔可夫链采样算法识别B样条中简约的节点配置，同时在并行采样框架内基于边际似然进行状态数量选择。通过大量仿真研究，我们证明该方法在性能上优于其他替代方案，并展示其稳健性和可扩展性。我们还以白鳍鲨为例，展示了该方法在动物活动数据分析中的探索性应用。贝叶斯框架的灵活性还便于纳入更现实的假设，我们通过开发一种新颖的分层条件隐马尔可夫模型来分析人类昼夜节律与睡眠建模的行为数据，验证了这一优势。