2.7. Conditional Latin Hypercube Sampling (cLHS)

The conditional Latin Hypercube Sampling (cLHS) is a prominent model-based sampling method that employs a stratified random technique to optimize sample selection using continuous and/or categorical covariates as input (Minasny and McBratney 2006). The cLHS is frequently utilized in digital soil mapping and soil property prediction applications (Ng et al., 2018). When compared to Monte Carlo sampling, the cLHS has proven to improve the sampling scheme and reduce the computational overhead (Yin et al., 2011). In a benchmark study on comparison of sampling techniques, Santos and Beck (2015) found that, while Importance Sampling and Subset Simulation were efficient sampling techniques in Monte Carlo Simulation, the use of Latin Hypercube Sampling had a significant and positive influence for all sampling techniques.

We used the cLHS approach to select sample sizes – 100, 400, 700, and 1000 samples – from each input image index. We computed the sample sizes by doubling the confidence interval, starting at 2, then 4, and 8 in order to capture the potential variabilities in a gradient field. The cLHS procedure follows these steps (Minasny and McBratney 2006): Given N sites with ancillary data (W), select n sample sites (n ⪡ N) so that the sampled sites w form a Latin hypercube in the feature space, or the multivariate distribution of W is maximally stratified. For k continuous variables (e.g., image index), each component of W is divided into n (e.g., sample size = 1000) equally probable strata based on their distributions, and w is a sub-sample of W.