On an approximate optimality criterion for the design of field experiments under spatial dependence

Abstract

The design of large-scale field trials where the residuals are correlated has been of recent interest, in large part because of advances in statistical and computational methods of analysis. The construction of designs for correlated data has typically used A-optimality and is computationally intensive. This involves calculating the inverse of the information matrix for treatments under the supervision of an optimization strategy that explores the design space. We propose an approximation to A-optimality, using nearest-neighbour balance, that is less computationally demanding and can achieve at least 95% efficiency relative to A-optimality in many practical situations.