![]() ![]() 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.In two dimensions the difference between random sampling, Latin hypercube sampling, and orthogonal sampling can be explained as follows: Another advantage is that random samples can be taken one at a time, remembering which samples were taken so far. This sampling scheme does not require more samples for more dimensions (variables) this independence is one of the main advantages of this sampling scheme. When sampling a function of N, to be equal for each variable. 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. 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. Detailed computer codes and manuals were later published. An independently equivalent technique was proposed by Vilnis Eglājs in 1977. LHS was described by Michael McKay of Los Alamos National Laboratory in 1979. The sampling method is often used to construct computer experiments or for Monte Carlo integration. The proof is similar to that of Theorem 3 and is omitted here.Latin hypercube sampling ( LHS) is a statistical method for generating a near-random sample of parameter values from a multidimensional distribution. Hence we have that the sum of elementwise product of \(p_1, p_2\) and \(p_3\), no matter whether they are distinct or not, is equal to zero, which implies the second-order orthogonality of \(P_c\). Ye KQ, Li W, Sudjianto A (2000) Algorithmic construction of optimal symmetric Latin hypercube desings. Ye KQ (1998) Orthogonal column Latin hypercubes and their application in computer designs. Yang JY, Liu MQ (2012) Construction of orthogonal and nearly orthogonal Latin hypercube designs from orthogonal designs. Sun FS, Liu MQ, Lin DKJ (2009) Construction of orthogonal Latin hypercube designs. Steinberg DM, Lin DKJ (2006) A construction method for orthogonal Latin hypercube designs. Santner TJ, Williams BJ, Notz WI (2003) The design and analysis of computer experiments. Pang F, Liu MQ, Lin DKJ (2009) A construction method for orthogonal Latin hypercube designs with prime power levels. McKay MD, Beckman RJ, Conover WJ (1979) A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Lin CD, Mukerjee R, Tang B (2009) Construction of orthogonal and nearly orthogonal Latin hypercube designs. Lin CD, Bingham D, Sitter RR, Tang B (2010) A new and flexible method for constructing designs for computer experiments. Technometrics 49:45–55įang KT, Li R, Sudjianto A (2006) Design and modeling for computer experiments. Commun Stat Theory Methods 34:417–428Ĭioppa TM, Lucas TW (2007) Efficient nearly orthogonal and space-filling Latin hypercubes. Biometrika 96:51–65īutler NA (2005) Supersaturated Latin hypercube designs. ![]() Bingham D, Sitter RR, Tang B (2009) Orthogonal and nearly orthogonal designs for computer experiments. ![]()
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