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

Authors:
Budiman Minasny;Alex B. McBratney
Affiliations:
Australian Centre for Precision Agriculture, Faculty of Agriculture, Food and Natural Resources, The University of Sydney, Australia;Australian Centre for Precision Agriculture, Faculty of Agriculture, Food and Natural Resources, The University of Sydney, Australia
Venue:
Computers & Geosciences
Year:
2006

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Abstract

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.