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A Bayesian Framework for Quantifying Uncertainty in Stochastic Simulation

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A Bayesian Framework for Quantifying Uncertainty in Stochastic Simulation. / Xie, Wei; Nelson, Barry Lee; Barton, Russell.
In: Operations Research, Vol. 62, No. 6, 01.12.2014, p. 1439-1452.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

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Xie W, Nelson BL, Barton R. A Bayesian Framework for Quantifying Uncertainty in Stochastic Simulation. Operations Research. 2014 Dec 1;62(6):1439-1452. Epub 2014 Oct 21. doi: 10.1287/opre.2014.1316

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Xie, Wei ; Nelson, Barry Lee ; Barton, Russell. / A Bayesian Framework for Quantifying Uncertainty in Stochastic Simulation. In: Operations Research. 2014 ; Vol. 62, No. 6. pp. 1439-1452.

Bibtex

@article{60768341daa54a80aa52debaf02bc91a,
title = "A Bayesian Framework for Quantifying Uncertainty in Stochastic Simulation",
abstract = "When we use simulation to estimate the performance of a stochastic system, the simulation often contains input models that were estimated from real-world data; therefore, there is both simulation and input uncertainty in the performance estimates.In this paper, we provide a method to measure the overall uncertainty while simultaneously reducing the influence of simulation estimation error due to output variability. To reach this goal, a Bayesian framework is introduced. We use a Bayesian posterior for the input-model parameters, conditional on the real-world data, to quantify the input-parameter uncertainty; we propagate this uncertainty to the output mean using a Gaussian process posterior distribution for thesimulation response as a function of the input-model parameters, conditional on a set of simulation experiments. We summarize overall uncertainty via a credible interval for the mean. Our framework is fully Bayesian, makes more effective use of the simulation budget than other Bayesian approaches in the stochastic simulation literature, and is supported with both theoretical analysis and an empirical study. We also make clear how to interpret our credible interval and why it is distinctly different from the confidence intervals for input uncertainty obtained in other papers.",
keywords = "simulation output analysis, Gaussian process, metamodel, input uncertainty, Bayesian inference",
author = "Wei Xie and Nelson, {Barry Lee} and Russell Barton",
year = "2014",
month = dec,
day = "1",
doi = "10.1287/opre.2014.1316",
language = "English",
volume = "62",
pages = "1439--1452",
journal = "Operations Research",
issn = "0030-364X",
publisher = "INFORMS Inst.for Operations Res.and the Management Sciences",
number = "6",

}

RIS

TY - JOUR

T1 - A Bayesian Framework for Quantifying Uncertainty in Stochastic Simulation

AU - Xie, Wei

AU - Nelson, Barry Lee

AU - Barton, Russell

PY - 2014/12/1

Y1 - 2014/12/1

N2 - When we use simulation to estimate the performance of a stochastic system, the simulation often contains input models that were estimated from real-world data; therefore, there is both simulation and input uncertainty in the performance estimates.In this paper, we provide a method to measure the overall uncertainty while simultaneously reducing the influence of simulation estimation error due to output variability. To reach this goal, a Bayesian framework is introduced. We use a Bayesian posterior for the input-model parameters, conditional on the real-world data, to quantify the input-parameter uncertainty; we propagate this uncertainty to the output mean using a Gaussian process posterior distribution for thesimulation response as a function of the input-model parameters, conditional on a set of simulation experiments. We summarize overall uncertainty via a credible interval for the mean. Our framework is fully Bayesian, makes more effective use of the simulation budget than other Bayesian approaches in the stochastic simulation literature, and is supported with both theoretical analysis and an empirical study. We also make clear how to interpret our credible interval and why it is distinctly different from the confidence intervals for input uncertainty obtained in other papers.

AB - When we use simulation to estimate the performance of a stochastic system, the simulation often contains input models that were estimated from real-world data; therefore, there is both simulation and input uncertainty in the performance estimates.In this paper, we provide a method to measure the overall uncertainty while simultaneously reducing the influence of simulation estimation error due to output variability. To reach this goal, a Bayesian framework is introduced. We use a Bayesian posterior for the input-model parameters, conditional on the real-world data, to quantify the input-parameter uncertainty; we propagate this uncertainty to the output mean using a Gaussian process posterior distribution for thesimulation response as a function of the input-model parameters, conditional on a set of simulation experiments. We summarize overall uncertainty via a credible interval for the mean. Our framework is fully Bayesian, makes more effective use of the simulation budget than other Bayesian approaches in the stochastic simulation literature, and is supported with both theoretical analysis and an empirical study. We also make clear how to interpret our credible interval and why it is distinctly different from the confidence intervals for input uncertainty obtained in other papers.

KW - simulation output analysis

KW - Gaussian process

KW - metamodel

KW - input uncertainty

KW - Bayesian inference

U2 - 10.1287/opre.2014.1316

DO - 10.1287/opre.2014.1316

M3 - Journal article

VL - 62

SP - 1439

EP - 1452

JO - Operations Research

JF - Operations Research

SN - 0030-364X

IS - 6

ER -