M. D. McKay, R. J. Beckman, and W. J. Conover. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometr i cs, 21(2):239--245, 1979. 34  Home/Search   Document Not in Database   Summary   Related Articles   Check

....linear or quadratic functions. We want to be able to generate designs somewhat automatically, and we would like to be able to generate designs for irregular (nonrectangular) feasible regions. We have opted for designs that are used in quasi Monte Carlo integration: Latin hypercube sampling (LHS) [27, 35], orthogonal arrays (OA) 28] and LHS [36] In LHS, each of the n variables is chosen from d equally spaced values. The we use are space filling in the following sense: the variables in the experimental design are assigned from l distinct values. In every subset of k variables every one of ....

M. D. McKay, W. J. Conover, and R. J. Beckman, A comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics, 21 (1979), pp. 239--245.

....coordinate. Conversely if the vertical coordinate is the more important one, then it would be better to take one point from each of 16 horizontal strata. It is possible to stratify both ways with the same sample, in what is known as Latin hypercube sampling (McKay, Beckman and W. J. Conover [24]) or n rooks 0.2 0.4 0.6 0.8 1.0 1.2 0.6 0.4 0.2 0.0 0.2 0.4 0.6 Figure 1.2: The upper plot shows a piece wise smooth function f on [0, 1) The step function is the best approximation f to f , in mean square error, among functions constant over intervals [j 10, j 1) 10) The ....

M. D. McKay, R. J. Beckman, and W. J. Conover. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 21(2):239--45, 1979.

....Monte Carlo sampling, in which all # are independent of each other, then = # (x) N , where # (x) Var[F (x, #(#) We also used Latin Hypercube sampling (LHS) to construct the sampleaverage function fN . In this technique, initially proposed by McKay, Beckman, and Conover [22], a sample of size N is constructed by dividing the interval (0, 1) into N subintervals of equal size and picking one number randomly from each subinterval. These N numbers are then shu#ed, and the resulting sequence is used to generate random variates for a given distribution, possibly by ....

M. D. McKay, R. J. Beckman, and W. J. Conover. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 21:239--245, 1979.

....more significant. Related techniques include analysis of variance (ANOVA) 51] and primary effects analysis, in which the parameters which have the greatest influence on the results are identified from sampling results. 9. 2 LHS The Latin hypercube sampling method was developed by McKay, et al. [46] as an alternative to random sampling. Under certain monotonicity conditions associated with the function to be sampled, Latin hypercube sampling provides a more accurate estimate of the mean value than does random sampling. That is, given an equal number of samples, the LHS estimate of the mean ....

....LHS techniques, in general, require fewer samples than traditional Monte Carlo for the same accuracy in statistics, but they still can be prohibitively expensive. For further information on the method and its relationship to other sampling techniques, one is referred to the works by McKay, et al. [46], Iman and Shortencarier [43] and Helton and Davis [41] 10.2.1 Uncertainty Quantification Example using Sampling Methods The following response functions from the Textbook example problem (see Chapter 20) 1) 2) 3) will be used to demonstrate the application of sampling methods for ....

McKay, M. D., Beckman, R. J., and Conover, W. J., "A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code," Technometrics, Vol. 21, No. 2, 1979, pp. 239-245.

....did verify Condition 3 for this example. 10 Example 5 Latin Hypercube Sampling. This method uses the randomized point set (# (i) n, # (i) n) y i , i =0, n 1 , where the # j s are i.i.d. uniform permutations of [0, 1, n 1] and the y i s are i.i.d. uniform over [0, 1 n) [3, 19, 22]. We can interpret # as the randomness needed to generate all the # j s and y i s. Here, all pairs (u i , u j )fori j have the same joint distribution and all pairs (u i , u i ) have the same joint distribution. Thus, Condition 3 holds for any ordering of the u i s. Example 6 Digitally ....

M. D. Mckay, R. J. Beckman, and W. J. Conover. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 21:239--245, 1979.

.... Num ; The probability distributions of the stochastic variables is used to bias the construction of these scenarios. We also implemented one of the best sampling methods from experimental design, and one of the best scenario reduction methods from operations research. Latin hypercube sampling [McKay et al. 1979] , ensures that a range of values for a variable are sampled. Suppose we want n sample scenarios. We divide the unit interval into n intervals, and sample a value for each stochastic variable whose cumulative probability occurs in each of these interval. We then construct n sample scenarios from ....

M. D. McKay, R. J. Beckman, and W. J. Conover. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 21(2):239--245, 1979.

....distribution of design sites is defined by all di#erent combinations of j = # j k u j ,k j =0,1, # j , where the are integers. If all # j = #, then the number of these design points is (# 1) 4.2. Latin Hypercube Sampling Latin hypercube sampling, due to McKay et al. [5], is a strategy for generating random sample points ensuring that all portions of the vector space is represented. Consider the case where we wish to sample m points in the n dimensional vector space . The Latin hypercube sampling strategy is as follows: 1. Divide the interval of each dimension ....

M.D. McKay, W.J. Conover, R.J. Beckman, A comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code, Technometrics, vol. 21, no. 2, 1979.

....in which samples are taken at different points in the design space , the dimensions of which are the design variables. Taking a sample is akin to performing a circuit simulation. The sampling method is a heuris tic, multistage experiment (see Figure 2) that uses Latin Hypercube Sampling [9] in each iteration. Resampling after the first iteration depends on the evaluation of the prediction error, measured by cross validation. The predictor function is a data interpo]ant. Interpolation is performed using Moving Least Square Interpola tion [6] on the simulated points. The predictor ....

M.D. McKay, R. J. Beckman, and W. J. Conover. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 21(2):239-245, May 1979.

....The P Algorithm is a formalization of an intuitive search strategy, and in fact, provides a framework for devising global optimization algorithms. We now describe our particular implementation of the P Algorithm. 1. Choose k points zi, i = 1, k uniformly from A using Latin Hypercube Sampling [9] and compute ( z) by simulation. Start iteration 1 = 1. 2. Using the BLUP and MSE expression in [15] see Appendix 1, equations 17 and 19) find the mean m(zj) and variance s(zj) at N k uniformly distributed points in A. 3. Find the smallest value of m(x) i.e. m, c) minjcl. N m(zj) ....

....input transitions (see figure 3) and the delal(c) is the largest delay over these input transitions. D, is the maximum delay constraint. The models for delay and skew were initially established by simulating k = 100 different sizing schemes, selected randomly using Latin Hypercube Sampling [9]. The first row of table 1 shows the sizing scheme with the best skew value, satisfying the delay constraint, among these 100 points. This sizing scheme is not feasible. The second row shows the nearest feasible point to this sizing and the delay and skew value for that circuit. Since the number ....

M.D. McKay, R. J. Beckman, and W. J. Conover. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 21(2):239-245, May 1979.

....of design sites is defined by all di#erent combinations of i = # j k u j q j ,k i =0, 1, q j , where the q are integers. If all q j = q, then the number of these design points is (q 1) 4.2. Latin Hypercube Sampling Latin hypercube sampling, due to McKay et al. [3], is a strategy for generating random sample points ensuring that all portions of the vector space is represented. Consider the case where we wish to sample m points in the n dimensional vector space# . The Latin hypercube sampling strategy is as follows: 1. Divide the interval of each ....

M.D. McKay, W.J. Conover, R.J. Beckman, A comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code, Technometrics, vol. 21, no. 2, 1979.

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M. D. McKay, R. J. Beckman, and W. J. Conover. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometr i cs, 21(2):239--245, 1979. 34

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M. D. McKay, W. J. Conover, and R. J. Beckman. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 21:239--245, 1979.

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McKay, M. D., Conover, W. J. and Beckman, R. J. (1979). A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code, Technometrics, 21, 239-245

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McKay, M.D., Beckman, R.J., Conover, W.J., 1979. "A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code," Technometrics, Vol. 21, No. 2, pp. 239-245.

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M. D. McKay, R. J. Bechman, and W. J. Conover, "A comparison of three methods for selecting values of input variables in the analysis of output from a computer code", Technomet., Vol 21, no 2 May 1979.

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M. D. McKay, R. J. Beckman, and W. J. Conover. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometr i cs, 21(2):239--245, 1979. 34

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M. D. McKay, R. J. Beckman, and W. J. Conover. A comparison of three methods of selecting values of input variables in the analysis of output from a computer code. Technometrics, 21:239--245, 1979.

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McKay, M.D., Beckman, R.J., Conover, W.J., "A Comparison of Three Methods For Selecting Values of Input Variables in the Analysis of Output From a Computer Code," Technometrics, Vol. 21, No. 2, 1979, pp. 239-245.

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McKay, M.D., Beckman, R.J., Conover, W.J., "A Comparison of Three Methods for Selecting Values of Input Variables iin the Analysis of Output From a Computer Code", Technometrics, Vol. 21, No. 2, 1979, pp. 239-245.

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McKay, M.D., Beckman, R.J., Conover, W.J., "A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code," Technometrics, Vol. 21, No. 2, 1979, pp. 239-245.

No context found.

M. D. McKay, R. J. Beckman and W. J. Conover, "A comparison of three methods for selecting values of input variables in the analysis of output from a computer code", Technometrics, Vol. 21, No. 2, pp.239-245, 1979.

No context found.

M. D. McKay, R. J. Beckman, and W. J. Conover. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 21:239--245, 1979.

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McKay, M.D., Beckman, R.J. and Conover, W.J., 1979, "A comparison of three methods for selecting values of input variables in the analysis of output from a computer code," Technometrics, 21(2), 239-45.

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McKay, M. D., Conover, W. J. and Beckman, R. J. (1979). A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code. Technometrics, 21, 239--245.

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M. D. McKay, R. J. Beckman, and W. J. Conover, "A comparison of three methods of selecting values of input variables in the analysis of output from a computer code," Technometrics 21, pp. 239--245, 1979.

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