In this paper, we present a theoretical and computational workflow for the non-parametric Bayesian inference of drift and diffusion functions of autonomous diffusion processes. We base the inference on the partial differential equations arising from the infinitesimal generator of the underlying process. Following a problem formulation in the infinite-dimensional setting, we discuss optimization- and sampling-based solution methods. As preliminary results, we showcase the inference of a single-scale, as well as a multiscale process from trajectory data.

翻译：本文提出了一种用于自主扩散过程漂移与扩散函数非参数贝叶斯推断的理论与计算流程。该推断方法基于底层过程无穷小生成元导出的偏微分方程。在建立无限维空间中的问题表述后，我们讨论了基于优化与采样的求解方法。作为初步结果，我们展示了从轨迹数据中推断单尺度过程与多尺度过程的实例。