变系数随机微分方程及其在生态学中的应用
Varying-coefficient stochastic differential equations with applications in ecology
摘要：
随机微分方程（SDEs）是数学金融学、物理学和生物学等许多领域分析时间序列数据的常用工具。它们提供了感兴趣的现象的机理描述，并且它们的参数通常有明确的解释。这些优点的代价是需要一个相对简单的模型规范。我们提出了一个灵活的模型与时变动态的参数的过程是协变量的非参数函数，类似于广义可加模型。结合的SDES和非参数的方法允许的ESTA捕捉更详细的，非静态的，数据生成过程的功能。我们提出了一种计算效率高的近似推理方法，其中的插值参数可以根据固定协变量效应，随机效应，或基础惩罚平滑样条。我们展示了这种方法的多功能性和实用性与生态学中的三个应用程序，在那里往往是一个建模的可解释性和灵活性之间的权衡。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
