Optimal designs for Gaussian process models |via spectral decomposition

• We use the Karhunen–Loève expansion of a Gaussian process to derive mathematical expressions to several objective functions of interest.
• We proceed to suggest optimal experimental designs for the GP model.
• We demonstrate our results via a worked example.
• We perform error analysis.

Gaussian processes provide a popular statistical modelling approach in various fields, including spatial statistics and computer experiments. Strategic experimental design could prove to be crucial when data are hard to collect. We use the Karhunen–Loève decomposition to study several popular design criteria. The resulting expressions are useful for understanding and comparing the criteria. A truncated form of the expansion is used to generate optimal designs. We give detailed results, including an error analysis, for the well-established integrated mean squared prediction error design criterion.