An Insight into the Data Structure of the Dynamic Batch Means Algorithm with Binary Tree Code

Batching is a well-known method used to estimate the variance of the sample mean in steady-state simulation. Dynamic batching is a novel technique employed to implement traditional batch means estimators without the knowledge of the simulation run length a priori. In this study, we reinvestigated th...

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Bibliographic Details
Published inMathematics (Basel) Vol. 7; no. 9; p. 791
Main Author Chih, Mingchang
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.09.2019
Subjects
Algorithms
Binary codes
binary tree code
Closed form solutions
Coding
Data structures
dynamic batch means
estimation
Exact solutions
Mathematical analysis
Mathematics
Simulation
variance of the sample mean
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Summary:Batching is a well-known method used to estimate the variance of the sample mean in steady-state simulation. Dynamic batching is a novel technique employed to implement traditional batch means estimators without the knowledge of the simulation run length a priori. In this study, we reinvestigated the dynamic batch means (DBM) algorithm with binary tree hierarchy and further proposed a binary coding idea to construct the corresponding data structure. We also present a closed-form expression for the DBM estimator with binary tree coding idea. This closed-form expression implies a mathematical expression that clearly defines itself in an algebraic binary relation. Given that the sample size and storage space are known in advance, we can show that the computation complexity in the closed-form expression for obtaining the indexes c j ( k ) , i.e., the batch mean shifts s , is less than the effort in recursive expression.
ISSN:2227-7390
2227-7390
DOI:10.3390/math7090791