Efficient Prediction Designs for Random Fields

TL;DR

This paper develops new design algorithms for empirical kriging that balance accuracy and cost, especially when traditional space-filling designs are inadequate, demonstrated through simulations and real data.

Contribution

It introduces two novel algorithms based on a compound criterion for quasi-optimal design in empirical kriging, addressing limitations of existing space-filling approaches.

Findings

Algorithms effectively identify near-optimal designs for empirical kriging.

Proposed methods outperform traditional space-filling designs in accuracy and cost.

Validated on simulated and real oceanographic data.

Abstract

For estimation and predictions of random fields it is increasingly acknowledged that the kriging variance may be a poor representative of true uncertainty. Experimental designs based on more elaborate criteria that are appropriate for empirical kriging are then often non-space-filling and very costly to determine. In this paper, we investigate the possibility of using a compound criterion inspired by an equivalence theorem type relation to build designs quasi-optimal for the empirical kriging variance, when space-filling designs become unsuitable. Two algorithms are proposed, one relying on stochastic optimization to explicitly identify the Pareto front, while the second uses the surrogate criteria as local heuristic to chose the points at which the (costly) true Empirical Kriging variance is effectively computed. We illustrate the performance of the algorithms presented on both a simple simulated example and a real oceanographic dataset.