This chapter presents specific aspects of Gaussian process modeling in the presence of complex noise. Starting from the standard homoscedastic model, various generalizations from the literature are presented: input varying noise variance, non-Gaussian noise, or quantile modeling. These approaches are compared in terms of goal, data availability and inference procedure. A distinction is made between methods depending on their handling of repeated observations at the same location, also called replication. The chapter concludes with the corresponding adaptations of the sequential design procedures. These are illustrated in an example from epidemiology.

翻译：本章探讨了在复杂噪声存在下高斯过程建模的特定方面。从标准同方差模型出发，介绍了文献中的多种推广方法：输入变化噪声方差、非高斯噪声或分位数建模。这些方法在目标、数据可用性和推断过程方面进行了比较。根据对同一位置重复观测（也称为复制）的处理方式，对方法进行了区分。本章最后讨论了序贯设计程序的相应调整，并以流行病学中的一个示例加以说明。