Convex and Monotonic Bootstrapped Kriging
AbstractAbstract: 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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Bibliographic InfoPaper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2012-066.
Date of creation: 2012
Date of revision:
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Web page: http://center.uvt.nl
Distribution-free bootstrapping; Gaussian process; random simulation; sensitivity analysis; optimization; confidence intervals;
Other versions of this item:
- C0 - Mathematical and Quantitative Methods - - General
- C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
- C9 - Mathematical and Quantitative Methods - - Design of Experiments
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
- C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
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- Kleijnen, Jack P.C. & Beers, W.C.M. van, 2009.
"Monotonicity-Preserving Bootstrapped Kriging Metamodels for Expensive Simulations,"
2009-75, Tilburg University, Center for Economic Research.
- J P C Kleijnen & W C M van Beers, 2013. "Monotonicity-preserving bootstrapped Kriging metamodels for expensive simulations," Journal of the Operational Research Society, Palgrave Macmillan, vol. 64(5), pages 708-717, May.
- Kleijnen, Jack P.C. & Beers, W.C.M. van, 2013. "Monotonicity-preserving bootstrapped kriging metamodels for expensive simulations," Open Access publications from Tilburg University urn:nbn:nl:ui:12-5904627, Tilburg University.
- Kleijnen, J.P.C., 2008. "Review of the book [Design and Analysis of Simulation Experiments]," Open Access publications from Tilburg University urn:nbn:nl:ui:12-4379049, Tilburg University.
- Kleijnen, Jack P.C., 2013. "Simulation-Optimization via Kriging and Bootstrapping: A Survey (Revision of CentER DP 2011-064)," Discussion Paper 2013-064, Tilburg University, Center for Economic Research.
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