Convex and Monotonic Bootstrapped Kriging

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

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Abstract

Abstract: Distribution-free bootstrapping of the replicated responses of a given discreteevent 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 simulationoptimization 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
Place of PublicationTilburg
PublisherInformation Management
Number of pages26
Volume2012-066
Publication statusPublished - 2012

Publication series

NameCentER Discussion Paper
Volume2012-066

Fingerprint

Kriging
Monotonic
Metamodel
Bootstrapping
Confidence interval
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
Traffic

Keywords

  • Distribution-free bootstrapping
  • Gaussian process
  • random simulation
  • sensitivity analysis
  • optimization
  • confidence intervals

Cite this

Kleijnen, J. P. C., Mehdad, E., & van Beers, W. C. M. (2012). Convex and Monotonic Bootstrapped Kriging. (CentER Discussion Paper; Vol. 2012-066). Tilburg: Information Management.
Kleijnen, Jack P.C. ; Mehdad, E. ; van Beers, W.C.M. / Convex and Monotonic Bootstrapped Kriging. Tilburg : Information Management, 2012. (CentER Discussion Paper).
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Kleijnen, JPC, Mehdad, E & van Beers, WCM 2012 'Convex and Monotonic Bootstrapped Kriging' CentER Discussion Paper, vol. 2012-066, Information Management, Tilburg.

Convex and Monotonic Bootstrapped Kriging. / Kleijnen, Jack P.C.; Mehdad, E.; van Beers, W.C.M.

Tilburg : Information Management, 2012. (CentER Discussion Paper; Vol. 2012-066).

Research output: Working paperDiscussion paperOther research output

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AU - Mehdad, E.

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N2 - Abstract: Distribution-free bootstrapping of the replicated responses of a given discreteevent 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 simulationoptimization 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.

AB - Abstract: Distribution-free bootstrapping of the replicated responses of a given discreteevent 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 simulationoptimization 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.

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Kleijnen JPC, Mehdad E, van Beers WCM. Convex and Monotonic Bootstrapped Kriging. Tilburg: Information Management. 2012. (CentER Discussion Paper).