Accurate emulators for large-scale computer experiments

TL;DR

This paper introduces a multi-step procedure for building accurate emulators in large-scale computer experiments, improving interpolation accuracy through theoretical error bounds and decomposition.

Contribution

It develops a theoretical framework for understanding and bounding errors in multi-step emulators, demonstrating their potential for substantial accuracy improvements.

Findings

Bounds on numeric and nominal errors are established.

Multi-step approach significantly improves interpolation accuracy.

Theoretical analysis supports practical effectiveness of the method.

Abstract

Large-scale computer experiments are becoming increasingly important in science. A multi-step procedure is introduced to statisticians for modeling such experiments, which builds an accurate interpolator in multiple steps. In practice, the procedure shows substantial improvements in overall accuracy, but its theoretical properties are not well established. We introduce the terms nominal and numeric error and decompose the overall error of an interpolator into nominal and numeric portions. Bounds on the numeric and nominal error are developed to show theoretically that substantial gains in overall accuracy can be attained with the multi-step approach.