Simulation output analysis using integrated paths II

Abstract

This article is a sequel to a previous article that introduced a class of variance estimators for steady-state simulation output analysis. The estimators were constructed by applying a quadratic function to a vector obtained from iterated integrations of the simulation output. The previous article concentrated on deriving the limiting distributions of the estimators and on their computational efficiency for a particular choice of quadratic function. The present article considers estimators constructed from different quadratic functions, chosen mainly to reduce bias compared to the estimators of the previous article. Overlapping and nonoverlapping batch means versions of the estimators are discussed. ACM Reference Format:Calvin, J. M. 2009. Simulation output analysis using integrated paths II: Low bias estimators. ACM Trans. Model.

Brownian bridge and statistical error estimation in Monte Carlo reactor calculation

“…Hence, Equation ( 15) has been proven. The above proof of Equation ( 15) is, to this author's opinion, more streamlined than Calvin's arguments [12] and shows some technical details such as the derivation of Equation ( 16), the presentations of Equations ( 19) and ( 21), and the separate proof for the case of r = 0.…”

“…In this work, on-the-fly error estimation with fixed storage size is investigated based on the iterated integration of simulation output (IISO) [12]. Here, the IISO methodology has been chosen because it can be applied to any correlated series from an identical distribution.…”

“…Therefore, on-the-fly error estimation is desired, which can compute σ 2 at any generations except some initial generations. Recently, the following on-the-fly algorithm with fixed storage size was proposed by Calvin [12]. Calvin's algorithm for the computation of σ 2…”

“…At each n, the computation of σ 2 costs O(k 2 ) operations of additions and multiplications. Calvin [12] has shown that the matrix L n can be uniquely determined within an outputprocessing framework of iterated integrations and there exists freedom in the choice of the symmetric positive definite matrix Q. For the former reason, Calvin's algorithm is termed IISO as referred to earlier.…”

“…In this section, stepwise interpolation is consistently utilized as seen in Equation ( 5), while linear interpolation is argued by Calvin [12]. Note that Equation ( 5) can be rewritten as…”