Gaussian processes (GPs) are sophisticated distributions to model functional data. Whilst theoretically appealing, they are computationally cumbersome except for small datasets. We implement two methods for scaling GP inference in Stan: First, a general sparse approximation using a directed acyclic dependency graph. Second, a fast, exact method for regularly spaced data modeled by GPs with stationary kernels using the fast Fourier transform. Based on benchmark experiments, we offer guidance for practitioners to decide between different methods and parameterizations. We consider two real-world examples to illustrate the package. The implementation follows Stan's design and exposes performant inference through a familiar interface. Full posterior inference for ten thousand data points is feasible on a laptop in less than 20 seconds.

翻译：Gausian 进程( GPs) 是用于模拟功能数据的复杂分布。 在理论上很有吸引力, 它们在计算上是繁琐的, 除了小数据集。 我们用两种方法在 Stan 中测量 GP 的推论: 首先, 使用定向的单向依赖性图谱进行一般的稀疏近近似。 第二, 由 GPs 以固定内核建模的定期空间数据快速精确的方法 。 根据基准实验, 我们为实践者提供指南, 供他们决定不同的方法和参数化。 我们考虑两个真实世界的例子来说明软件包。 执行时遵循 Stan 的设计, 并通过熟悉的界面显示性能推论 。 在不到20秒的时间内, 膝上型电脑上可以完全推断一万个数据点 。