A conditioned Latin hypercube method for sampling in the presence of ancillary information

This paper presents the conditioned Latin hypercube as a sampling strategy of an area with prior information represented as exhaustive ancillary data. Latin hypercube sampling (LHS) is a stratified random procedure that provides an efficient way of sampling variables from their multivariate distributions. It provides a full coverage of the range of each variable by maximally stratifying the marginal distribution. For conditioned Latin hypercube sampling (cLHS) the problem is: given N sites with ancillary variables (X), select x a sub-sample of size n (n << N) in order that x forms a Latin hypercube, or the multivariate distribution of X is maximally stratified. This paper presents the cLHS method with a search algorithm based on heuristic rules combined with an annealing schedule. The method is illustrated with a simple 3-D example and an application in digital soil mapping of part of the Hunter Valley of New South Wales, Australia. Comparison is made with other methods: random sampling, and equal spatial strata. The results show that the cLHS is the most effective way to replicate the distribution of the variables. (c) 2006 Elsevier Ltd. All rights reserved.