Gaussian processes that can be decomposed into a smooth mean function and a stationary autocorrelated noise process are considered and a fully automatic nonparametric method to simultaneous estimation of mean and auto-covariance functions of such processes is developed. Our empirical Bayes approach is data-driven, numerically efficient and allows for the construction of confidence sets for the mean function. Performance is demonstrated in simulations and real data analysis. The method is implemented in the R package eBsc that accompanies the paper.

翻译：高斯进程可以分解成平稳平均功能和固定的与自动有关的噪声过程,并开发出一种完全自动的非参数方法来同时估计这些过程的中值和自动变量功能。我们的经验性贝斯方法以数据为驱动,数字效率高,并允许为中值功能构建信任套件。在模拟和真实数据分析中演示性能。该方法在伴随纸张的 R 包 eBsc 中实施。