A Finite-Memory Algorithm for Batch Means Estimators in Simulation Output Analysis

Abstract

A classic problem of stochastic simulation is estimating the variance of point estimators, the prototype estimator being the sample mean from a steady-state autocorrelated process. The traditional batch means (BM) estimator requires knowledge of the sample size a priori. This paper proposes an algorithm to implement certain BM estimators without knowing the sample size in advance. The proposed algorithm is useful when the run length is random or is extremely long in simulation models.Index Terms-Batch means estimators, mean squared error, variance of the sample mean.

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

“…Yeh and Schmeiser [18] were the first to introduce the dynamic batching idea into NBM. Song [14] further proposed a general form for the (100 f )% DOBM estimator using a recursive expression, where [15,16,19] have been recently developed for steady-state simulation output analysis.…”

“…is defined in Equation (4). Song [14] derived a proposition to show that DBM is equivalent to the traditional BM for some cases via a recursive expression:…”

“…Dynamic batch means (DBM) estimators use Fishman's idea [13] of periodically doubling batch sizes as sampling procedures. DBM estimators [14][15][16] use only finite storage space (i.e., fixed memory), increase batch size dynamically as simulation run length increases, and compute the batch means estimates according to the value of the current batch size. DBM estimators require only O(1) storage space and no knowledge of the simulation run length a priori.…”

“…DBM estimators require only O(1) storage space and no knowledge of the simulation run length a priori. Song [14] proposed the dynamic overlapping batch means estimator (DOBM), which allows users to implement the traditional overlapping batch means estimator (OBM) for (100 f )% overlapping cases without knowing the sample size in advance, where f = 0 [14] also showed that DOBM and OBM are equivalent in terms of data structure properties using the recursive relationships.…”

Estimación de la Esperanza, Varianza y Cuantiles en Simulaciones de Estado Estable

“…Los tres métodos que se comparan en este estudio son (i) B: una sola corrida (larga), dividiendo la corrida en grupos (sin espacio entre grupos) para calcular el error de estimación (Law, 2014), (ii) SB: una sola corrida, dividiendo la corrida en grupos e incluyendo espacio entre grupos (Song, 2011) para calcular el error de estimación, y (iii) MR: método de repeticiones con calentamiento antes de cada repetición (Law, 1977). En particular, se discute el desempeño de estos tres métodos en la simulación del tiempo en la fila de espera de una cola M/M/1, considerando el ancho medio del intervalo de confianza (IC) asintótico como medida del error de estimación.…”