Revisit the Dynamic-Batch-Means Estimator

模擬輸出分析中動態重疊分批估計式之改善

楊子寬(Tsu-Kuang Yang) ； 桑慧敏(Whey-Ming Song) ； 遲銘璋(Ming-Chang Chih)

《工業工程學刊》 26卷6期 (2009/11) Pp. 499-509

https://doi.org/10.29977/JCIIE.200911.0008

摘要

在模擬學領域中，估計樣本平均數變異數是一個相當重要的課題。傳統的分批估計式(batch means estimators)在使用上有其限制，也就是必須事先預知或給定此次模擬實驗的樣本觀察値數目(simulation run length)才可使用。目前文獻中，僅存在兩個樣本平均數變異數估計式可以利用固定儲存空間(constant storage space)來突破此限制：動態不重疊分批估計式(dynamic non-overlapping batch means, DNBM)與動態重疊分批估計式(dynamic partial-overlapping batch means estimator, DPBM)。以統計績效均方誤(meansquared error)而言，動態重疊分批估計式的表現比動態不重疊分批估計式來得好，但是動態重疊分批估計式所需要用來儲存樣本觀察値的空間是動態不重疊分批估計式的四倍。本研究提出了一個改善後的動態重疊分批估計式，其所需要的儲存空間與動態不重疊分批估計式相同。

關鍵字

樣本平均數變異數 ； 分批估計式 ； 均方誤

並列摘要

Estimating the variance of the sample mean is a classical problem of stochastic simulation. Traditional batch means estimators require specification of the simulation run length a priori. To our knowledge, the dynamic non-overlapping batch means estimator (DNBM) and dynamic partial-overlapping batch means estimator (DPBM) are the only two existing variance estimators requiring a constant storage space for any sample size. The performance of the DPBM is better than that of DNBM in terms of the mse criteria, but the DPBM requires four times more memory than the DNBM. This paper improves the DPBM by developing a computational version of the DPBM that requires the same storage space as the DNBM estimator.

並列關鍵字

variance of the sample mean ； batch means estimators ； mean squared error

參考文獻

Aktaran-Kalayc, T.,C. Alexopoulos,N. T. Argon,D. Goldsman,J. R. Wilson(2007).Exact expected values of variance estimators for simulation.Naval Research Logistics.54,397-410.

Conway, R. W.(1963).Some tactical problems in digital simulation.Management Science.6,92-110.

Crane, M. A.,D. L. Iglehart(1975).Simulating stable stochastic systems Ⅲ: Regenerative process and discrete-event simulations.Operations Research.23,33-45.

Ferguson, N. M.,D. A. Cummings,C. Fraser,J. C. Cajka,P. C. Cooley,D. S. Burke(2006).Strategies for mitigating an influenza pandemic.Nature.442,448-452.

Fishman, G. S.,L. S. Yarberry(1997).An implementation of the batch means method.INFOEMS.9,296-310.