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Discrete-event simulation models generate random variates from input distributions and compute outputs according to the simulation logic. The input distributions are typically fitted to finite real-world data and thus are subject to estimation errors that can propagate to the simulation outputs: an issue commonly known as input uncertainty (IU). This paper investigates quantifying IU using the output confidence intervals (CIs) computed from bootstrap quantile estimators. The standard direct bootstrap method has overcoverage due to convolution of the simulation error and IU; however, the brute-force way of washing away the former is computationally demanding. We present two new bootstrap methods to enhance direct resampling in both statistical and computational efficiencies using shrinkage strategies to down-scale the variabilities encapsulated in the CIs. Our asymptotic analysis shows how both approaches produce tight CIs accounting for IU under limited input data and simulation effort along with the simulation sample-size requirements relative to the input data size. We demonstrate performances of the shrinkage strategies with several numerical experiments and investigate the conditions under which each method performs well. We also show advantages of nonparametric approaches over parametric bootstrap when the distribution family is misspecified and over metamodel approaches when the dimension of the distribution parameters is high. History: Accepted by Bruno Tuffin, Area Editor for Simulation. Funding: This work was supported by the National Science Foundation [CAREER CMMI-1834710, CAREER CMMI-2045400, DMS-1854659, and IIS-1849280]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0044 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0044 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .
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Subsampling to Enhance Efficiency in Input Uncertainty Quantification
In stochastic simulation, input uncertainty refers to the output variability arising from the statistical noise in specifying the input models. This uncertainty can be measured by a variance contribution in the output, which, in the nonparametric setting, is commonly estimated via the bootstrap. However, due to the convolution of the simulation noise and the input noise, the bootstrap consists of a two-layer sampling and typically requires substantial simulation effort. This paper investigates a subsampling framework to reduce the required effort, by leveraging the form of the variance and its estimation error in terms of the data size and the sampling requirement in each layer. We show how the total required effort can be reduced from an order bigger than the data size in the conventional approach to an order independent of the data size in subsampling. We explicitly identify the procedural specifications in our framework that guarantee relative consistency in the estimation and the corresponding optimal simulation budget allocations. We substantiate our theoretical results with numerical examples.
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- Award ID(s):
- 1834710
- PAR ID:
- 10324825
- Date Published:
- Journal Name:
- Operations Research
- ISSN:
- 0030-364X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1287/opre.2021.2168
