J. Sacks, W.J. Welch, T.J. Mitchell, and H.P. Wynn. Design and analysis of computer experiments. Statistical Science, 4:409--435, 1989. Home/Search Document Not in Database Summary Related Articles Check |
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A Rigorous Framework for Optimization of Expensive Functions by.. - Booker (1998) (23 citations) (Correct)
....useful information from s. The problem of choosing a set of initial design sites, x 1 , x d #B, is a problem in the design of experiments. This problem has been studied extensively in the recent literature on the design and analysis of computer experiments (DACE) surveys of which include [31, 2, 22]. We seek designs that are space filling (for lack of a better term) i.e. that will allow us to sample the behavior of the objective function throughout the feasible region. We want to avoid designs that are tied to a narrow class of approximating functions, e.g. linear or quadratic ....
....(MLE) and thereby to specify a well defined procedure for selecting s. Although MLE has been criticized in the spatial statistics literature, e.g. 30] it has been defended by others as a crude form of cross validation [19, 10] Our experience to date has been similar to that reported in [31]: crude MLE s lead to useful prediction. Assuming that the covariances in question are a constant unknown variance times unknown correlations of a specified form, there exist closed form expressions for the MLEs of the mean and variance parameters. To obtain MLEs of the correlation ....
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J. Sacks, W. J. Welch, T. J. Mitchell, and H. P. Wynn, Design and analysis of computer experiments, Statistical Science, 4 (1989), pp. 409--423.
Managing Surrogate Objectives to - Optimize Helicopter Rotor (Correct)
....versions of one of the target problems for our collaboration, the design of a lower vibration helicopter rotor blade. The two versions are a 31 variable problem and an 11 variable problem. The smaller problem was obtained from the larger problem by an analysis of variance decomposition, or ANOVA, [9, 12, 13] performed on a kriging interpolatory model of the objective function [15, 61. The details of the ANOVA decomposition and the way the 11 variables were determined is covered elsewhere by Andrew Booker in this specially organized section. To us, ANOVA identifies the design parameters that have the ....
J. Sacks, W. J. Welch, T. J. Mitchell, and H. P. Wynn. Design and analysis of computer experi- ments. Statistical Science, 4(4):409-435, 1989.
Optimization Using Surrogate - Objectives On Helicopter (Correct)
....adjusted locally to some extent as new points are added. They are motivated by the supposition that the output being modeled is a realization of a Gaussian spatial process. Called kriging models, they are recommended in the Design and Analysis of Computer Experiments (DACE) literature, surveyed in [20]. These models are made to interpolate the observations, and they depend on a set of correlation parameters [20] that we estimated via maximum likelihood estimation (MLE) as in [9] In [13, 9] it is shown that MLE can be thought of as a form of cross validation. This Gaussian process ....
....modeled is a realization of a Gaussian spatial process. Called kriging models, they are recommended in the Design and Analysis of Computer Experiments (DACE) literature, surveyed in [20] These models are made to interpolate the observations, and they depend on a set of correlation parameters [20] that we estimated via maximum likelihood estimation (MLE) as in [9] In [13, 9] it is shown that MLE can be thought of as a form of cross validation. This Gaussian process supposition is a convenient fiction ( 23] that provides useful error estimates, termed mean squared errors (rose) ....
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J. Sacks, W. J. Welch, T. J. Mitchell, and H. P. Wynn. Design and analysis of computer experiments. Statistical Science, 4(4):409-435, 1989.
Chemical Library Subset Selection Algorithms: A.. - Hamprecht, Thiel.. (Correct)
....only on the covariance function and on the location of the design points y i , i = 1, n, but not on the responses Z(y i ) the question of optimal design can be discussed without knowledge of the actual response. The question remains which design criterion to choose. Natural choices are [23] . Minimization of the integrated mean square error SK (x)dx . Minimization of the maximum mean square error max x#R # SK (x) x 0.2 0.4 0.6 0.8 1 Figure 5: Weight # 1 (x) of the left design point in Fig. 4. Maximization of the prior entropy ## g(#) log g(#)d# where g(#) is ....
....for a weight function #(x) which, for the time being, may be set to 1 minimization of the integrated mean square error is equivalent to maximization of #(x)# (x)# 1 #(x)dx = # i (x)Cov(x, y i )dx (6) which is reminiscent of an unnormalized distortion in vector quantization. In [23], the maximization was e#ected with a quasi Newton optimizer. In analogy to the Linde Buzo Gray [24] and the Rose Gurewitz Fox [25] algorithm, we propose to minimize the contribution to the prediction error from each design point 13 2 0 2 4 4 2 0 2 4 0 0.5 1 4 2 0 2 4 ....
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Sacks, J.; Welch, W. J.; Mitchell, T. J.; Wynn, H. P. Design and analysis of computer experiments (with discussion). Stat. Sci. 1989. 4 , 409--435.
DACE - A MATLAB Kriging Toolbox - Lophaven, Nielsen, Søndergaard (2002) (Correct)
....is assumed to satisfy the normalization conditions [S : j ] 0, V S : j ,S : j =1,j=1, n , Y : j ] 0, V Y : j ,Y : j =1,j=1, q , 2.1) where X : j is the vector given by the jth column in matrix X, and [ and V , denote respectively the mean and the covariance. Following [9] we adopt a model y that expresses the deterministic response y(x) for an n dimensional input x#D#IR , as a realization of a regression model The user does not have to think of this: The first step in the model construction is to normalize the given S, Y so that (2.1) is satisfied, see ....
....denotes the size of the matrix and O is the matrix of all zeros) constant : J f = O n1 ] linear : J f = O n1 I nn ] quadratic : J f = O n1 I nn H] where we illustrate H 1) by n =2: H= 2x 1 x 2 0 0 x 1 2x 2 n=3: H= 2x 1 x 2 x 3 000 0x 102 x 2x 3 0 00x 10x 22 x 3 . As [9] we restrict our attention to correlations of the form R(#,w,x) j (#, w j x j ) i.e. to products of stationary, one dimensional correlations. More specific, the toolbox contains the following 7 choices Name j (#, d j ) exp exp( # j expg exp( # j #n 1 ) 0 # n 1 gauss ....
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J. Sacks, W.J. Welch, T.J. Mitchell, H.P. Wynn, Design and Analysis of Computer Experiments, Statistical Science, vol. 4, no. 4, pp. 409-435, 1989.
Global Optimization Approach to Transistor Sizing for.. - Mehrotra, Franzon, Liu (1993) (Correct)
....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) 9) Let Yo: m, z) e, At each z5 find the probability Pj(Yo) p 4. Choose mt points with largest ....
J. Sacks, W. J. Welch, T. J. Mitchell, and H. P. Wynn. Design and analysis of computer experiments. Statistical Science, 4(4):pp. 409-435, 1989.
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J. Sacks, W.J. Welch, T.J. Mitchell, and H.P. Wynn. Design and analysis of computer experiments. Statistical Science, 4:409--435, 1989.
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J. Sacks, W. J. Welch, T. J. Mitchell and H. P. Wynn, "Design and Analysis of Computer Experiments ". Statistical Science, 4(4):409--435, 1989.
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J. Sacks, W. J. Welch, T. J. Mitchell, and H. P. Wynn. Design and analysis of computer experiments. Statistical Science, 4(4):409--435, 1989.
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J. Sacks, W. J. Welch, T. J. Mitchell, and H. P. Wynn, "Design and analysis of computer experiments," Statistical Science, vol. 4, no. 4, pp. 409--435, 1989.
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Sacks, J., Welch, W.J., Mitchell, W.J., Wynn, H.P.: Design and analysis of computer experiments. Statistical Science 4 (1989) 409--435
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J. Sacks, W. J. Welch, T. J. Mitchell, and H. P. Wynn. Design and analysis of computer experiments. Statistical Science, 4(4):409--435, 1989.
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J. Sacks, W.J. Welch, T.J. Mitchell, and H.P. Wynn. Design and Analysis of Computer Experiments. Statistical Science, Vol. 4(4):pages 409--435, 1989.
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J. Sacks, W.J. Welch, T.J. Mitchell, and H.P. Wynn. Design and Analysis of Computer Experiments. Statistical Science, Vol. 4(4):pages 409--435, 1989.
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J. Sacks, W.J. Welch, W.J. Mitchell, and H.P. Wynn. Design and analysis of computer experiments. Statistical Science, 4(4):409--435, 1989. (with discussion) .
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J. Sacks, W. J. Welch, T. J Mitchell, and H. P. Wynn. Design and analysis of computer experiments. Statistical Science, 4(4):409--423, 1989.
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J. Sacks, W. J. Welch, T. J. Mitchell, and H. P. Wynn. Design and analysis of computer experiments. Statistical Science, 4(4):409--435, 1989.
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Sacks J, Welch W J, Mitchell T J, Wynn H P (1989) Design and Analysis of Computer Experiments. Statistical Science, Vol. 4, No. 4, pp. 409-435
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J. Sacks, W. J. Welch, T. J. Mitchell and H. P. Wynn, 1989, "Designs and analysis of computer experiments", Statistical Science, Vol. 4, No. 4, pp. 409--423.
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J. Sacks, W. J. Welch, T. J. Mitchell, H. P. Wynn, Design and analysis of computer experiments (c/r: P423-435), Statistical Science 4 (1989) 409-423.
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Sacks, J., Welch, W. J., Mitchell, T. J. and Wynn, H. P., 1989, "Design and analysis of computer experiments," Statistical Science, 4(4), 409-435.
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- Sacks, J. Welch, W. J., Mitchell T. J., Wynn, H. M., 1989: Design and Analysis of Computer Experiments. Statistical Science, Volume 4, Issue 4. November 1989. pp 409-423.
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Sacks, J.; Welch, W. J.; Mitchell, T. J.; Wynn, H. P. Design and Analysis of Computer Experiments. Statistical Science 1989, 4 , 409.
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