Latin Hypercube Sampling Explained Manuals Were Later
A Latin hypercube is the generalisation of this concept to an arbitrary number of dimensions, whereby each sample is the only one in each axis-aligned hyperplane containing it.When sampling a function of N , to be equal for each variable. Through a representative example, it is shown that the proposed sampling technique provides.In the context of statistical sampling, a square grid containing sample positions is a Latin square if (and only if) there is only one sample in each row and each column. Latin Hypercube and Low Discrepancy sampling methods, and. Detailed computer codes and manuals were later published. Iman and coauthors in 1981. It was further elaborated by Ronald L.
Such configuration is similar to having N rooks on a chess board without threatening each other. In Latin hypercube sampling one must first decide how many sample points to use and for each sample point remember in which row and column the sample point was taken. One does not necessarily need to know beforehand how many sample points are needed. In random sampling new sample points are generated without taking into account the previously generated sample points. Another advantage is that random samples can be taken one at a time, remembering which samples were taken so far.In two dimensions the difference between random sampling, Latin hypercube sampling, and orthogonal sampling can be explained as follows:
Riga: Zinatne Publishing House: 104–107. Problems of Dynamics and Strengths. "New approach to the design of multifactor experiments". American Statistical Association. "A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code". All sample points are then chosen simultaneously making sure that the total set of sample points is a Latin hypercube sample and that each subspace is sampled with the same density.Thus, orthogonal sampling ensures that the set of random numbers is a very good representative of the real variability, LHS ensures that the set of random numbers is representative of the real variability whereas traditional random sampling (sometimes called brute force) is just a set of random numbers without any guarantees.
Latin hypercube sampling (program user's guide). Doi: 10.1080/00224065.1981.11978748. Journal of Quality Technology. Introduction, input variable selection and preliminary variable assessment".
"Orthogonal column Latin hypercubes and their application in computer experiments". "Orthogonal arrays for computer experiments, integration and visualization". Journal of the American Statistical Association.
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