Optimizing the design of a latin hypercube sampling estimator

Alexander J. Zolan, John J. Hasenbein, David Morton

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Stratified sampling and Latin hypercube sampling (LHS) reduce variance, relative to naïve Monte Carlo sampling, by partitioning the support of a random vector into strata. When creating these estimators, we must determine: (i) the number of strata; and, (ii) the partition that defines the strata. In this paper, we address the second point by formulating a nonlinear optimization model that designs the strata to yield a minimum-variance stratified sampling estimator. Under a discrete set of candidate boundary points, the optimization model can be solved via dynamic programming. We extend this technique to LHS, using an approximation of estimator variance to obtain strata for the domain of a multivariate function. Empirical results show significant variance reduction compared to using equal-probability strata for LHS or naïve Monte Carlo sampling.

Original languageEnglish (US)
Title of host publication2017 Winter Simulation Conference, WSC 2017
EditorsVictor Chan
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1832-1843
Number of pages12
ISBN (Electronic)9781538634288
DOIs
StatePublished - Jan 4 2018
Event2017 Winter Simulation Conference, WSC 2017 - Las Vegas, United States
Duration: Dec 3 2017Dec 6 2017

Publication series

NameProceedings - Winter Simulation Conference
ISSN (Print)0891-7736

Other

Other2017 Winter Simulation Conference, WSC 2017
CountryUnited States
CityLas Vegas
Period12/3/1712/6/17

Fingerprint

Latin Hypercube Sampling
Stratified Sampling
Monte Carlo Sampling
Sampling
Estimator
Optimization Model
Variance Reduction
Multivariate Functions
Minimum Variance
Variance Estimator
Nonlinear Optimization
Random Vector
Dynamic Programming
Nonlinear Model
Partitioning
Partition
Approximation
Design
Dynamic programming

ASJC Scopus subject areas

  • Software
  • Modeling and Simulation
  • Computer Science Applications

Cite this

Zolan, A. J., Hasenbein, J. J., & Morton, D. (2018). Optimizing the design of a latin hypercube sampling estimator. In V. Chan (Ed.), 2017 Winter Simulation Conference, WSC 2017 (pp. 1832-1843). (Proceedings - Winter Simulation Conference). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/WSC.2017.8247920
Zolan, Alexander J. ; Hasenbein, John J. ; Morton, David. / Optimizing the design of a latin hypercube sampling estimator. 2017 Winter Simulation Conference, WSC 2017. editor / Victor Chan. Institute of Electrical and Electronics Engineers Inc., 2018. pp. 1832-1843 (Proceedings - Winter Simulation Conference).
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abstract = "Stratified sampling and Latin hypercube sampling (LHS) reduce variance, relative to na{\"i}ve Monte Carlo sampling, by partitioning the support of a random vector into strata. When creating these estimators, we must determine: (i) the number of strata; and, (ii) the partition that defines the strata. In this paper, we address the second point by formulating a nonlinear optimization model that designs the strata to yield a minimum-variance stratified sampling estimator. Under a discrete set of candidate boundary points, the optimization model can be solved via dynamic programming. We extend this technique to LHS, using an approximation of estimator variance to obtain strata for the domain of a multivariate function. Empirical results show significant variance reduction compared to using equal-probability strata for LHS or na{\"i}ve Monte Carlo sampling.",
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Zolan, AJ, Hasenbein, JJ & Morton, D 2018, Optimizing the design of a latin hypercube sampling estimator. in V Chan (ed.), 2017 Winter Simulation Conference, WSC 2017. Proceedings - Winter Simulation Conference, Institute of Electrical and Electronics Engineers Inc., pp. 1832-1843, 2017 Winter Simulation Conference, WSC 2017, Las Vegas, United States, 12/3/17. https://doi.org/10.1109/WSC.2017.8247920

Optimizing the design of a latin hypercube sampling estimator. / Zolan, Alexander J.; Hasenbein, John J.; Morton, David.

2017 Winter Simulation Conference, WSC 2017. ed. / Victor Chan. Institute of Electrical and Electronics Engineers Inc., 2018. p. 1832-1843 (Proceedings - Winter Simulation Conference).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Zolan AJ, Hasenbein JJ, Morton D. Optimizing the design of a latin hypercube sampling estimator. In Chan V, editor, 2017 Winter Simulation Conference, WSC 2017. Institute of Electrical and Electronics Engineers Inc. 2018. p. 1832-1843. (Proceedings - Winter Simulation Conference). https://doi.org/10.1109/WSC.2017.8247920