We study integration and reconstruction of Gaussian random functions with inhomogeneous local smoothness. A single realization may only be observed at a finite sampling design and the correct local smoothness is unknown. We construct adaptive two-stage designs that lead to asymptotically optimal methods. We show that every nonadaptive design is less efficient.
"Spatial adaption for predicting random functions." Ann. Statist. 26 (6) 2264 - 2288, December 1998. https://doi.org/10.1214/aos/1024691470