Utility functions implemented in SSNdesign.

Empirical utility functions are utility functions where the covariance parameters are estimated from data simulated using the prior draws. θ = a vector of covariance parameters from a geostatistical model; and y = data that is either directly observed from a process or simulated from it. OP = optimal design; AD = adaptive design. n/a = no covariance parameters involved. I(θ) = the expected Fisher Information Matrix; ; . sz = a prediction site; S = the set of all prediction sites. . . Ot(θ) = a summary statistic from the existing design. D(xi, xj) = the distance between two points xi and xj. The distance can be measured as Euclidean distance or hydrological distance along the stream network [10]. D = a sorted vector of non-zero distances in a distance matrix; J = the number of times each distance occurs in one triangle of the matrix. The subscript w = 1, 2, …, W counts the W unique non-zero entries in the distance matrix. p = a weighting power, with p ≥ 1. In the Empirical column, × means No, ✓ means Yes.