Latin hypercube sampling: Difference between revisions

Revision as of 20:16, 21 August 2016

Revision as of 19:48, 24 March 2017

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When sampling a function of <math>N</math> variables, the range of each variable is divided into <math>M</math> equally probable intervals. <math>M</math> sample points are then placed to satisfy the Latin hypercube requirements; note that this forces the number of divisions, <math>M</math>, to be equal for each variable. Also note that this sampling scheme does not require more samples for more dimensions (variables); this independence is one of the main advantages of this sampling scheme. Another advantage is that random samples can be taken one at a time, remembering which samples were taken so far.

The maximum number of combinations for a Latin Hypercube of <math>M</math> divisions and <math>N</math> variables (i.e., dimensions) can be computed with the following formula:

<math>\left(\prod_{n=0}^{M-1} (M-n)\right)^{N-1} = (M!)^{N-1}</math>

For example, a Latin hypercube of <math>M = 4</math> divisions with <math>N = 2</math> variables (i.e., a square) will have 24 possible combinations. A Latin hypercube of <math>M = 4</math> divisions with <math>N = 3</math> variables (i.e., a cube) will have 576 possible combinations.

'''Orthogonal sampling''' adds the requirement that the entire sample space must be sampled evenly. Although more efficient, orthogonal sampling strategy is more difficult to implement since all random samples must be generated simultaneously.

[[Image:LHSsampling.png|100px|right]]