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.
翻译:在数学融资、物理和生物学等许多领域,Stochactic discripal 等方程式是分析时间序列数据的流行工具,它们提供了对相关元素的机械性描述,其参数往往有明确的解释。这些优势是以要求相对简单的模型规格为代价的。我们为具有时间变化动态的SDE提出一个灵活的模型,其中过程参数是同源变量的非参数,类似于通用添加模型。将SDE与非参数方法结合起来,使得SDE能够捕捉数据生成过程更为详细、非静止的特征。我们提出了一个计算高效的近似推论方法,其中SDE参数可以根据固定的共变法效应、随机效应或基边际平滑螺纹而变化。我们展示了这一方法在三个生态应用中的多功能和实用性,其中往往在可解释性和灵活性之间有一种模拟交易。