Operations Research · 1982 · 372 citations · 12 references
Public HealthBiostatisticsExperimental DesignSimulation-based DesignStatisticsConfidence IntervalsInferential StatisticsResampling MethodsResampling TechniquesSimulation MethodsStatistical InferenceAssumptions AnalysisBatch Size AnalysisConfidence Interval EstimationConfidence Interval EvaluationIndependenceSample Size CalculationScientific Experiment SimulationSimulation Experiment Design
Batching is a common technique for estimating confidence intervals on the mean of correlated simulation outputs, but recent work has shown that using too small batch sizes can violate normality and independence assumptions, leading to incorrect coverage probabilities. This study quantifies the impact of employing batch sizes larger than necessary to meet normality and independence assumptions. Using oversized batches produces correct coverage but increases the expected half‑length, its variability, and the probability of covering non‑mean points; the effect is pronounced with fewer than ten batches, diminishes after about thirty, and additional batches have smaller influence, especially at lower confidence levels, and the results also guide the use of independent replications for mean confidence intervals.
Batching is a commonly used method for calculating confidence intervals on the mean of a sequence of correlated observations arising from a simulation experiment. Several recent papers have considered the effect of using batch sizes too small to satisfy assumptions of normality and/or independence, and the resulting incorrect probabilities of the confidence interval covering the mean. This paper quantifies the effects of using batch sizes larger than necessary to satisfy normality and independence assumptions. These effects include (1) correct probability of covering the mean, (2) an increase in expected half length, (3) an increase in the standard deviation and coefficient of variation of the half length, and (4) an increase in the probability of covering points not equal to the mean. For any sample size and independent and normal batch means, the results are (1) the effects of less than 10 batches are large and the effects of more than 30 batches small, and (2) additional batches have lesser effects on confidence intervals having lower confidence levels. The results also are useful in the context of using independent replications for establishing confidence intervals on the mean.
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Some Tactical Problems in Digital Simulation
R. W. Conway · Management Science · 1963 · 358 citations
Statistical Techniques in Simulation
Judy Walters, J.P.C. Kleijnen · Operational Research Quarterly (1970-1977) · 1976 · 347 citations
Business, Biostatistics, Mathematics +12