Optimal Mean-Squared-Error Batch Sizes

Song, Wheyming Tina; Schmeiser, Bruce W.

doi:10.1287/mnsc.41.1.110

Cited by 129 publications

(74 citation statements)

References 19 publications

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“…. Song and Schmeiser (1995) use the terms "balance point" and "center of gravity" to refer to the ratio γ 1 /(R 0 + γ 0 ) = γ 1 /σ 2 as a geometric characterization of the associated autocorrelation function. We also use the following notation: (i) p(n) = O(q(n)) means that there are positive constants c and n 0 such that 0 ≤ p(n) ≤ cq(n) for all n ≥ n 0 ; and (ii) p(n) = o(q(n)) means that lim n→∞ p(n)/q(n) = 0.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

SPSTS: A sequential procedure for estimating the steady-state mean using standardized time series

et al. 2016

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This article presents SPSTS, an automated sequential procedure for computing point and confidence-interval (CI) estimators for the steady-state mean of a simulation-generated process subject to user-specified requirements for the CI coverage probability and relative half-length. SPSTS is the first sequential method based on standardized time series (STS) area estimators of the steady-state variance parameter (i.e., the sum of covariances at all lags). Whereas its leading competitors rely on the method of batch means to remove bias due to the initial transient, estimate the variance parameter, and compute the CI, SPSTS relies on the signed areas corresponding to two orthonormal STS area variance estimators for these tasks. In successive stages of SPSTS, standard tests for normality and independence are applied to the signed areas to determine (i) the length of the warm-up period; and (ii) a batch size sufficient to ensure adequate convergence of the associated STS area variance estimators to their limiting chi-squared distributions. SPSTS's performance is compared experimentally with that of recent batch-means methods using selected test problems of varying degrees of difficulty. SPSTS performed comparatively well in terms of its average required sample size as well as the coverage and average half-length of the final CIs. ARTICLE HISTORYKEYWORDS Steady-state simulation; simulation output analysis; method of batch means; method of standardized time series; area variance estimator; nonoverlapping variance estimator; overlapping variance estimator uiie-3995r1-final.tex 1

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Section: Accepted Manuscriptmentioning

confidence: 99%

SPSTS: A sequential procedure for estimating the steady-state mean using standardized time series

et al. 2016

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“…In addition, the presence of two spatial Dirac delta functions corresponding to two path-dividing points 0:75r r j;iÀ1 þ 0:25r r j;i and 0:25r r j;iÀ1 þ 0:75r r j;i enables the reconstruction of the operand of T. Therefore, one is allowed to make a formal argument using the inverse of T. (20), Tê e ðmÞ C1 integrated over tally cell k is the fluctuating part of track length tally at tally cell k. Based on the definition of F in Eqs. (16) and (17) …”

Section: Derivation Of Arma Fitting For Track Length Estimatorsmentioning

confidence: 99%

Standard Deviation of Local Tallies in Global Monte Carlo Calculation of Nuclear Reactor Core

Ueki

2010

Journal of Nuclear Science and Technology

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Time series methodology has been studied to assess the feasibility of statistical error estimation in the continuous space and energy Monte Carlo calculation of the three-dimensional whole reactor core. The noise propagation was examined and the fluctuation of track length tallies for local fission rate and power has been formally shown to be represented by the autoregressive moving average process of orders p and, where p is an integer larger than or equal to two. Therefore, ARMA(p,p À 1) fitting was applied to the real standard deviation estimation of the power of fuel assemblies at particular heights. Numerical results indicate that straightforward ARMA(3,2) fitting is promising, but a stability issue must be resolved toward the incorporation in the distributed version of production Monte Carlo codes. The same numerical results reveal that the average performance of ARMA(3,2) fitting is equivalent to that of the batch method with a batch size larger than 100 and smaller than 200 cycles for a 1,100 MWe pressurized water reactor.

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“…Song and Schmeiser (1995) derived an approximation for the optimal batch size, m Ã , which minimizes the mean squared error of the variance estimator in batch means estimation procedures including UBM (but not WBM). They show empirically that this approximation tends to overestimate the optimal batch size and hence underestimate the optimal number of batches.…”

Section: Alternative Estimators and Interval Proceduresmentioning

confidence: 99%

Estimating the steady-state mean from short transient simulations

Sheth-Voss¹,

Willemain

Haddock

2005

European Journal of Operational Research

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Steady-state mean performance is a common basis for evaluating discrete event simulation models. However, analysis is complicated by autocorrelation and initial transients. We present confidence interval procedures for estimating the steady-state mean of a stochastic process from observed time series which may be short, autocorrelated, and transient. We extend the generalized least squares estimator of Snell and Schruben [IIE Trans. 17 (1985) 354] and develop confidence interval procedures for single and multiple-replication experiments. The procedures are asymptotically valid and, for short series with reasonable initializations (e.g., empty and idle), are comparable or superior to existing procedures. Further, we demonstrate and explain the robustness of the weighted batch means procedure of Bischak et al. [Manage. Sci. 39 (1993) 1002] to initialization bias. The proposed confidence interval procedure requires neither truncation of initial observations nor choice of batch size, and permits the existence of steady-state mean to be inferred from the data.

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Optimal Mean-Squared-Error Batch Sizes

Cited by 129 publications

References 19 publications

SPSTS: A sequential procedure for estimating the steady-state mean using standardized time series

SPSTS: A sequential procedure for estimating the steady-state mean using standardized time series

Standard Deviation of Local Tallies in Global Monte Carlo Calculation of Nuclear Reactor Core

Estimating the steady-state mean from short transient simulations

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