Convex and monotonic bootstrapped kriging

Jack P.C. Kleijnen, E. Mehdad, W.C.M. van Beers

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

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Abstract

Distribution-free bootstrapping of the replicated responses of a given discrete-event simulation model gives bootstrapped Kriging (Gaussian process) metamodels; we require these metamodels to be either convex or monotonic. To illustrate monotonic Kriging, we use an M/M/1 queueing simulation with as output either the mean or the 90% quantile of the transient-state waiting times, and as input the traffic rate. In this example, monotonic bootstrapped Kriging enables better sensitivity analysis than classic Kriging; i.e., bootstrapping gives lower MSE and confidence intervals with higher coverage and the same length. To illustrate convex Kriging, we start with simulation-optimization of an (s, S) inventory model, but we next switch to a Monte Carlo experiment with a second-order polynomial inspired by this inventory simulation. We could not find truly convex Kriging metamodels, either classic or bootstrapped; nevertheless, our bootstrapped “nearly convex” Kriging does give a confidence interval for the optimal input combination.
Original languageEnglish
Title of host publicationProceedings of the 2012 Winter Simulation Conference
EditorsC. Laroque, J. Himmelspach, R. Pasupathy, O. Rose, A.M. Uhrmacher
Place of PublicationBerlin
PublisherUnknown Publisher
Pages543-554
Publication statusPublished - 2012

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Kriging
Monotonic
Metamodel
Bootstrapping
Confidence interval
Simulation Optimization
Transient State
Distribution-free
Queueing
Monte Carlo Experiment
Inventory Model
Discrete Event Simulation
Quantile
Gaussian Process
Waiting Time
Sensitivity Analysis
Switch
Simulation
Simulation Model
Coverage

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Kleijnen, J. P. C., Mehdad, E., & van Beers, W. C. M. (2012). Convex and monotonic bootstrapped kriging. In C. Laroque, J. Himmelspach, R. Pasupathy, O. Rose, & A. M. Uhrmacher (Eds.), Proceedings of the 2012 Winter Simulation Conference (pp. 543-554). Berlin: Unknown Publisher.
Kleijnen, Jack P.C. ; Mehdad, E. ; van Beers, W.C.M. / Convex and monotonic bootstrapped kriging. Proceedings of the 2012 Winter Simulation Conference. editor / C. Laroque ; J. Himmelspach ; R. Pasupathy ; O. Rose ; A.M. Uhrmacher. Berlin : Unknown Publisher, 2012. pp. 543-554
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Kleijnen, JPC, Mehdad, E & van Beers, WCM 2012, Convex and monotonic bootstrapped kriging. in C Laroque, J Himmelspach, R Pasupathy, O Rose & AM Uhrmacher (eds), Proceedings of the 2012 Winter Simulation Conference. Unknown Publisher, Berlin, pp. 543-554.

Convex and monotonic bootstrapped kriging. / Kleijnen, Jack P.C.; Mehdad, E.; van Beers, W.C.M.

Proceedings of the 2012 Winter Simulation Conference. ed. / C. Laroque; J. Himmelspach; R. Pasupathy; O. Rose; A.M. Uhrmacher. Berlin : Unknown Publisher, 2012. p. 543-554.

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

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Kleijnen JPC, Mehdad E, van Beers WCM. Convex and monotonic bootstrapped kriging. In Laroque C, Himmelspach J, Pasupathy R, Rose O, Uhrmacher AM, editors, Proceedings of the 2012 Winter Simulation Conference. Berlin: Unknown Publisher. 2012. p. 543-554