### Abstract

Original language | English |
---|---|

Place of Publication | Tilburg |

Publisher | Information Management |

Number of pages | 26 |

Volume | 2012-066 |

Publication status | Published - 2012 |

### Publication series

Name | CentER Discussion Paper |
---|---|

Volume | 2012-066 |

### Fingerprint

### Keywords

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

### Cite this

*Convex and Monotonic Bootstrapped Kriging*. (CentER Discussion Paper; Vol. 2012-066). Tilburg: Information Management.

}

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

Research output: Working paper › Discussion paper › Other research output

TY - UNPB

T1 - Convex and Monotonic Bootstrapped Kriging

AU - Kleijnen, Jack P.C.

AU - Mehdad, E.

AU - van Beers, W.C.M.

N1 - Pagination: 26

PY - 2012

Y1 - 2012

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.

KW - Distribution-free bootstrapping

KW - Gaussian process

KW - random simulation

KW - sensitivity analysis

KW - optimization

KW - confidence intervals

M3 - Discussion paper

VL - 2012-066

T3 - CentER Discussion Paper

BT - Convex and Monotonic Bootstrapped Kriging

PB - Information Management

CY - Tilburg

ER -