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Estimation of Expectations and Variance Components in Two-Level Nested Simulation Experiments
Version 1
: Received: 8 May 2023 / Approved: 9 May 2023 / Online: 9 May 2023 (09:24:32 CEST)
A peer-reviewed article of this Preprint also exists.
Muñoz, D.F. Estimation of Expectations and Variance Components in Two-Level Nested Simulation Experiments. AppliedMath 2023, 3, 582-600. Muñoz, D.F. Estimation of Expectations and Variance Components in Two-Level Nested Simulation Experiments. AppliedMath 2023, 3, 582-600.
Abstract
When there is uncertainty in the value of parameters of the input random components of a stochastic simulation model, two-level nested simulation algorithms are used to estimate the expectation of performance variables of interest. In the outer level of the algorithm (n) observations are generated for the parameters, and in the inner level (m) observations of the simulation model are generated with the value of parameters fixed at the value generated in the outer level. In this article, we consider the case in which the observations at both levels of the algorithm are independent, showing how the variance of the observations can be decomposed into the sum of a parametric variance and a stochastic variance. Next, we derive central limit theorems that allow us to compute asymptotic confidence intervals to assess the accuracy of the simulation-based estimators for the point forecast and the variance components. Under this framework, we derive analytical expressions for the point forecast and the variance components of a Bayesian model to forecast sporadic demand; and we use these expressions to illustrate the validity of our theoretical results by performing simulation experiments using this forecast model.
Keywords
Bayesian forecasting; stochastic simulation; parameter uncertainty; two-level simulation
Subject
Computer Science and Mathematics, Computational Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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