Efficient prediction designs for random fields.

Area of Science:

• Geostatistics
• Applied Mathematics
• Data Science

Background:

• Kriging variance often inaccurately represents true uncertainty in random field estimation.
• Traditional experimental designs for empirical kriging (EK) can be non-space-filling and prohibitively expensive.
• Developing efficient and accurate experimental design criteria is crucial for reliable geostatistical predictions.

Purpose of the Study:

• To investigate a novel compound criterion for constructing quasi-optimal experimental designs for empirical kriging (EK).
• To address limitations of space-filling designs when estimating uncertainty in random fields.
• To propose and evaluate algorithms for generating these improved designs.

Main Methods:

• Development of a compound criterion inspired by equivalence theorem type relations.
• Implementation of two algorithms: one using stochastic optimization for Pareto front identification, and another employing surrogate criteria as local heuristics.
• Validation of algorithms using a simulated dataset and a real oceanographic dataset.

Main Results:

• The proposed compound criterion enables the construction of quasi-optimal designs for EK variance.
• The stochastic optimization algorithm effectively identifies the Pareto front for design criteria.
• The surrogate-based heuristic algorithm efficiently computes the true EK variance at selected points.
• Demonstrated performance on both simulated and real-world data.

Conclusions:

• The presented algorithms offer a viable alternative for experimental design in geostatistics, particularly when standard methods are inadequate.
• These methods improve the accuracy of uncertainty estimation in random fields.
• The approach provides a more cost-effective and efficient way to determine optimal experimental designs for empirical kriging.