论文标题
与生态学应用相关的随机微分方程不同
Varying-coefficient stochastic differential equations with applications in ecology
论文作者
论文摘要
随机微分方程（SDE）是在许多领域（例如数学金融，物理学和生物学）分析时间序列数据的流行工具。它们提供了对感兴趣现象的机械描述，并且它们的参数通常具有明确的解释。这些优势是以相对简单的模型规范为代价的。我们提出了一个具有随时间变化的动力学的SDE的灵活模型，其中该过程的参数是协变量的非参数函数，类似于广义加性模型。结合SDE和非参数方法，可以使SDE捕获数据生成过程的更详细，非平稳的特征。我们提出了一种近似推断的计算有效方法，其中SDE参数可以根据固定的协变量效应，随机效应或基本平滑光滑键变化。我们通过生态学的三种应用来证明这种方法的多功能性和效用，在这些应用程序中通常在可解释性和灵活性之间进行了建模权衡。
Stochastic differential equations (SDEs) are popular tools to analyse time series data in many areas, such as mathematical finance, physics, and biology. They provide a mechanistic description of the phenomeon of interest, and their parameters often have a clear interpretation. These advantages come at the cost of requiring a relatively simple model specification. We propose a flexible model for SDEs with time-varying dynamics where the parameters of the process are non-parametric functions of covariates, similar to generalized additive models. Combining the SDEs and non-parametric approaches allows for the SDE to capture more detailed, non-stationary, features of the data-generating process. We present a computationally efficient method of approximate inference, where the SDE parameters can vary according to fixed covariate effects, random effects, or basis-penalty smoothing splines. We demonstrate the versatility and utility of this approach with three applications in ecology, where there is often a modelling trade-off between interpretability and flexibility.
