Nonparametric inference in hidden Markov models using P-splines
Nonparametric inference in hidden Markov models using P-splines
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DOI：
10.1111/biom.12282
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发表时间：
2015-06-01
期刊：
影响因子：
1.9
通讯作者：
DeRuiter, Stacy L.
中科院分区：
文献类型：
--
作者：
Langrock, Roland;Kneib, Thomas;DeRuiter, Stacy L.
隐马尔可夫模型是一种灵活的时间序列模型，其中观测值的分布依赖于未观测到的序列相关状态。Hyndrome中的状态相关分布通常取自某类参数指定的分布。这个类的选择可能是困难的，一个不幸的选择可能会对状态估计产生严重的后果，更一般地说，会对模型的复杂性和解释产生严重的后果。我们证明了这些实际问题，在一个真实的数据应用程序与垂直速度的潜水喙鲸，我们表明，参数化的方法可以很容易地导致过于复杂的状态过程，阻碍有意义的生物推断。相比之下，对于潜水数据，具有非参数估计的状态相关分布的Hyndrome在状态数量方面更加简约，并且更容易解释，同时同样很好地拟合数据。我们的非参数估计方法是基于这样的想法，即将状态依赖分布的密度表示为大量标准化B样条基函数的线性组合，对非平滑性施加惩罚项，以保持拟合优度和平滑度之间的良好平衡。
Hidden Markov models (HMMs) are flexible time series models in which the distribution of the observations depends on unobserved serially correlated states. The state-dependent distributions in HMMs are usually taken from some class of parametrically specified distributions. The choice of this class can be difficult, and an unfortunate choice can have serious consequences for example on state estimates, and more generally on the resulting model complexity and interpretation. We demonstrate these practical issues in a real data application concerned with vertical speeds of a diving beaked whale, where we demonstrate that parametric approaches can easily lead to overly complex state processes, impeding meaningful biological inference. In contrast, for the dive data, HMMs with nonparametrically estimated state-dependent distributions are much more parsimonious in terms of the number of states and easier to interpret, while fitting the data equally well. Our nonparametric estimation approach is based on the idea of representing the densities of the state-dependent distributions as linear combinations of a large number of standardized B-spline basis functions, imposing a penalty term on non-smoothness in order to maintain a good balance between goodness-of-fit and smoothness.