Tensor-product interactions in Markov-switching models
马尔可夫转换模型中的张量积交互AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要明确研究潜在状态驱动的时间序列及马尔可夫转换模型的半参数扩展。
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马尔可夫转换模型中的张量积交互
- 研究问题
- 在由潜在状态驱动的时间序列模型中，如何突破单变量平滑函数的限制，灵活刻画协变量的多维交互及其对状态行为的影响？
- 方法与思路
- 作者将张量积交互纳入马尔可夫转换模型，从样条系数的随机效应表示出发，以扩展 Fellner–Schall 方法递归选择平滑程度。
- 材料陈述的贡献
- 摘要称框架容纳二维平滑、函数型随机效应和时空交互，提供自动平滑选择，并在三个生态案例及 LaMa R 包中实现。
- 阅读关注点
- 应核对交互项作用于哪些模型参数、惩罚与平滑参数更新、潜在状态可辨识性，以及大量参数时的收敛和计算表现。
- 阅读边界
- 这是 arXiv 预印本，同行评审与期刊接收未核实；摘要未说明稳健性的具体含义和计算基准，不能将潜在可扩展性当作普遍保证。
原文摘要
Markov-switching models are a powerful tool for modelling time series data that are driven by underlying latent states. As such, they are widely used in behavioural ecology, where discrete states can serve as proxies for behavioural modes and enable inference on latent behaviour driving e.g. observed movement. To understand drivers of behavioural changes, it is common to link model parameters to covariates. Over the last decade, nonparametric approaches have gained traction in this context to avoid unrealistic parametric assumptions. Nonetheless, existing methods are largely limited to univariate smooth functions of covariates, based on penalised splines, while real processes are typically complex requiring consideration of interaction effects. We address this gap by incorporating tensor-product interactions into Markov-switching models, enabling flexible modelling of multidimensional effects in a computationally efficient manner. Based on the extended Fellner-Schall method, we develop an efficient automatic smoothness selection procedure that is robust and scales well with the number of smooth functions in the model. The method builds on a random effects view of the spline coefficients and yields a recursive penalised likelihood procedure. As special cases, this general framework accommodates bivariate smoothing, function-valued random effects, and space-time interactions. We demonstrate its practical utility through three ecological case studies of an African elephant, common fruitflies, and Arctic muskoxen. The methodology is implemented in the LaMa R package, providing applied ecologists with an accessible and flexible tool for semiparametric inference in hidden-state models. The approach has the potential to drastically improve the level of detail in inference, allowing to fit HMMs with hundreds of parameters, 10-20 (potentially bivariate) smooths to thousands of observations.