Dynamic processes are crucial in many empirical fields, such as in oceanography, climate science, and engineering. Processes that evolve through time are often well described by systems of ordinary differential equations (ODEs). Fitting ODEs to data has long been a bottleneck because the analytical solution of general systems of ODEs is often not explicitly available. We focus on a class of inference techniques that uses smoothing to avoid direct integration. In particular, we develop a Bayesian smooth‐and‐match strategy that approximates the ODE solution while performing Bayesian inference on the model parameters. We incorporate in the strategy two main sources of uncertainty: the noise level of the measured observations and the model approximation error. We assess the performance of the proposed approach in an extensive simulation study and on a canonical data set of neuronal electrical activity.

中文翻译：

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常微分方程的贝叶斯平滑匹配理论对参数中的线性建模

在许多经验领域，例如海洋学，气候科学和工程学中，动态过程至关重要。随时间变化的过程通常由常微分方程（ODE）系统很好地描述。将ODE拟合到数据一直是瓶颈，因为通常无法明确获得ODE通用系统的分析解决方案。我们专注于使用平滑避免直接集成的一类推理技术。特别是，我们开发了一种贝叶斯平滑匹配策略，该策略在对模型参数执行贝叶斯推断时可以近似ODE解决方案。我们在策略中纳入了两个主要的不确定性来源：被测观测值的噪声水平和模型近似误差。