Spatial Designs

Sacks, Jerome; Schiller, Susannah B.

doi:10.1007/978-1-4612-3818-8_32

Cited by 44 publications

(28 citation statements)

References 8 publications

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“…Direct optimization can be performed using classical optimal design tools, such as simulated annealing (Sacks and Schiller, 1988;Morris and Mitchell, 1995), genetic algorithms (Hamada et al, 2001) or subset selection (Gramacy and Lee, 2009). However, when r × d is large, finding a good trade-off between exploration and local convergence is challenging.…”

Section: Nuclear Safety Test Casementioning

confidence: 99%

Fast Parallel Kriging-Based Stepwise Uncertainty Reduction With Application to the Identification of an Excursion Set

Chevalier¹,

Bect²,

Ginsbourger³

et al. 2014

Technometrics

111

132

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Stepwise Uncertainty Reduction (SUR) strategies aim at constructing a sequence of points for evaluating a function f in such a way that the residual uncertainty about a quantity of interest progressively decreases to zero. Using such strategies in the framework of Gaussian process modeling has been shown to be efficient for estimating the volume of excursion of f above a fixed threshold. However, SUR strategies remain cumbersome to use in practice because of their high computational complexity, and the fact that they deliver a single point at each iteration. In this paper we introduce several multi-point sampling criteria, allowing the selection of batches of points at which f can be evaluated in parallel. Such criteria are of particular interest when f is costly to evaluate and several CPUs are simultaneously available. We also manage to drastically reduce the computational cost of these strategies through the use of closed form formulas. We illustrate their performances in various numerical experiments, including a nuclear safety test case. Basic notions about kriging, auxiliary problems, complexity calculations, R code and datas are available online as supplementary materials.

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Section: Nuclear Safety Test Casementioning

confidence: 99%

Fast Parallel Kriging-Based Stepwise Uncertainty Reduction With Application to the Identification of an Excursion Set

Chevalier¹,

Bect²,

Ginsbourger³

et al. 2014

Technometrics

111

132

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“…In the case of (3) our robust optimality criterion is then analogous to the classical notion of I-optimality. In a similar vein, Sacks and Schiller (1988) considered the construction of designs, assuming that f 0 ðÁÞ and g 0 ðÁ; ÁÞ were correctly specified and that E XðtÞ ½ was known and 0. They used the loss function max t E½ða T t y À XðtÞÞ 2 , and remarked upon the lack of robustness, to changes in g 0 , of their procedures.…”

Section: Introductionmentioning

confidence: 99%

Robustness in spatial studies II: minimax design

Wiens

2005

Environmetrics

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SUMMARYWe consider robust methods for the construction of sampling designs in spatial studies. The designs are robust against misspecified regression responses, and are tailored for possible use with predictors which are minimax robust against misspecified variance/covariance structures. The loss function is based on the mean squared error of the predicted values. This is maximized, analytically, over a neighbourhood quantifying the departures from the fitted linear regression response. This maximum is then minimized numerically-by simulated annealing, or sequentially-in order to obtain the optimal designs.

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“…Several classic optimization techniques have already been employed to solve similar problems for optimal designs, for example simulated annealing [34], genetic algorithms [22], or treed optimization [20]. In our case such global approaches lead to a m × d dimensional problem and, since we do not rely on analytical gradients, the full optimization would be very slow.…”

Section: Algorithmmentioning

confidence: 99%

Quantifying Uncertainties on Excursion Sets Under a Gaussian Random Field Prior

Azzimonti¹,

Bect²,

Chevalier³

et al. 2016

SIAM/ASA J. Uncertainty Quantification

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We focus on the problem of estimating and quantifying uncertainties on the excursion set of a function under a limited evaluation budget. We adopt a Bayesian approach where the objective function is assumed to be a realization of a Gaussian random field. In this setting, the posterior distribution on the objective function gives rise to a posterior distribution on excursion sets. Several approaches exist to summarize the distribution of such sets based on random closed set theory. While the recently proposed Vorob'ev approach exploits analytical formulae, further notions of variability require Monte Carlo estimators relying on Gaussian random field conditional simulations. In the present work we propose a method to choose Monte Carlo simulation points and obtain quasi-realizations of the conditional field at fine designs through affine predictors. The points are chosen optimally in the sense that they minimize the posterior expected distance in measure between the excursion set and its reconstruction. The proposed method reduces the computational costs due to Monte Carlo simulations and enables the computation of quasi-realizations on fine designs in large dimensions. We apply this reconstruction approach to obtain realizations of an excursion set on a fine grid which allow us to give a new measure of uncertainty based on the distance transform of the excursion set. Finally we present a safety engineering test case where the simulation method is employed to compute a Monte Carlo estimate of a contour line.

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Spatial Designs

Cited by 44 publications

References 8 publications

Fast Parallel Kriging-Based Stepwise Uncertainty Reduction With Application to the Identification of an Excursion Set

Fast Parallel Kriging-Based Stepwise Uncertainty Reduction With Application to the Identification of an Excursion Set

Robustness in spatial studies II: minimax design

Quantifying Uncertainties on Excursion Sets Under a Gaussian Random Field Prior

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