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19
Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review
 Journal of the American Statistical Association
, 1996
"... A critical issue for users of Markov Chain Monte Carlo (MCMC) methods in applications is how to determine when it is safe to stop sampling and use the samples to estimate characteristics of the distribution of interest. Research into methods of computing theoretical convergence bounds holds promise ..."
Abstract

Cited by 223 (6 self)
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A critical issue for users of Markov Chain Monte Carlo (MCMC) methods in applications is how to determine when it is safe to stop sampling and use the samples to estimate characteristics of the distribution of interest. Research into methods of computing theoretical convergence bounds holds promise for the future but currently has yielded relatively little that is of practical use in applied work. Consequently, most MCMC users address the convergence problem by applying diagnostic tools to the output produced by running their samplers. After giving a brief overview of the area, we provide an expository review of thirteen convergence diagnostics, describing the theoretical basis and practical implementation of each. We then compare their performance in two simple models and conclude that all the methods can fail to detect the sorts of convergence failure they were designed to identify. We thus recommend a combination of strategies aimed at evaluating and accelerating MCMC sampler conver...
Advanced Methods For Simulation Output Analysis
, 1998
"... This paper reviews statistical methods for analyzing output data from computer simulations of single systems. In particular, it focuses on the problems of choosing initial conditions and estimating steadystate system parameters. The estimation techniques include the replication/deletion approach, t ..."
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Cited by 6 (2 self)
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This paper reviews statistical methods for analyzing output data from computer simulations of single systems. In particular, it focuses on the problems of choosing initial conditions and estimating steadystate system parameters. The estimation techniques include the replication/deletion approach, the regenerative method, the batch means method, and the standardized time series method.
Sequential Estimation of Quantiles
, 1998
"... Quantiles are convenient measures of the entire range of values of simulation outputs. However, unlike the mean and standard deviation, the observations have to be stored since calculation of quantiles requires several passes through the data. Thus, quantile estimation (QE) requires a large amount o ..."
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Cited by 3 (2 self)
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Quantiles are convenient measures of the entire range of values of simulation outputs. However, unlike the mean and standard deviation, the observations have to be stored since calculation of quantiles requires several passes through the data. Thus, quantile estimation (QE) requires a large amount of computer storage and computation time. Several approaches for estimating quantiles in RS (regenerative simulation) and nonRS, which can avoid the difficulties of QE, have been proposed in [Igl76], [Sei82b], and [JC85].
A Methodology for Initialisation Bias Reduction in Computer Simulation Output
, 1992
"... We present a new methodology for detecting when the steady state behaviour of a discretetime stochastic process has been approached after starting from a nontypical initial state. The main application and motivation for this method is the determination of a suitable truncation point for reduction ..."
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Cited by 2 (0 self)
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We present a new methodology for detecting when the steady state behaviour of a discretetime stochastic process has been approached after starting from a nontypical initial state. The main application and motivation for this method is the determination of a suitable truncation point for reduction of initialisation bias in computer simulation output. An implementation of this methodology is given which is most powerful for an exponential initial transient. Keywords: computer simulation, initialization bias This paper is based on the first author's Masters thesis at the Royal Melbourne Institute of Technology, Melbourne, Australia. y Centre for Signal Processing Research, QueenslandUniversity of Technology, Brisbane, Australia. Email: zsmajackway@qut.edu.au z Royal Melbourne Institute of Technology, Melbourne, Australia. 1 Introduction In computer simulation studies an estimate is often required for the steadystate mean of some quantity of interest. For each computer run the ...
Reducing The Variance Of Cycle Times In Semiconductor Manufacturing Systems
 In International Conference on Improving Manufacturing Performance in a Distributed Enterprise: Advanced Systems and Tools
, 1995
"... : In semiconductor manufacturing, due to rework and reentrant flow, overtaking of wafers can occur. The effect of overtaking is that cycle times at successive service centers are not mutually independent. As far as the distribution of cycle times is concerned, only higher moments are affected, the ..."
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Cited by 1 (1 self)
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: In semiconductor manufacturing, due to rework and reentrant flow, overtaking of wafers can occur. The effect of overtaking is that cycle times at successive service centers are not mutually independent. As far as the distribution of cycle times is concerned, only higher moments are affected, the mean cycle time remaining unchanged by the influence of overtaking. Further, in the literature, it is conjectured that variance of cycle times increases when overtaking increases. Taking into account this conjecture, we attempt at reducing the variability of cycle times by diminishing the magnitude of overtaking. This can be done by reversing the overtaking through appropriate sequencing rules. In order to achieve this goal, we examine several sequencing rules by means of simulation studies based on real data sampled at four different semiconductor manufacturing facilities. Our results elucidate that there is no general correlation between the magnitude of overtaking and the variance of cycl...
Rigorous Analysis of (Distributed) Simulation Results
 IEEE Transactions on Software Engineering
, 1989
"... Formal static analysis of the correctness and complexity of scalable and adaptive algorithms for distributed systems is difficult and often not appropriate. Rather, tool support is required to facilitate the 'trial and error' approach which is often adopted. Simulation supports this experimental app ..."
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Cited by 1 (1 self)
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Formal static analysis of the correctness and complexity of scalable and adaptive algorithms for distributed systems is difficult and often not appropriate. Rather, tool support is required to facilitate the 'trial and error' approach which is often adopted. Simulation supports this experimental approach well. In this paper we discuss the need for a rigorous approach to simulation results analysis and model validation. These aspects are often neglected in simulation studies, particularly in distributed simulation. Our aim is to provide the practitioner with a set of guidelines which can be used as a `recipe' in different simulation environments, making sound techniques (simulation and statistics) accessible to users. We demonstrate use of the suggested analysis method with two different distributed simulators (CNCSIM [8]) and (NEST[3]) thus illustrating its generality. The same guidelines may be used with other simulation tools to ensure meaningful results while obviating the need to a...
ABSTRACT A REPLICATION APPROACH TO INTERVAL ESTIMATION IN SIMULATION
"... In this study we modify an earlier approach developed for reducing the bias of the estimator for the mean response in simulation caused by the initial conditions. We try to balance the bias of the estimator in a simulation run by imposing a bias in the opposite direction in a companion run by suitab ..."
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In this study we modify an earlier approach developed for reducing the bias of the estimator for the mean response in simulation caused by the initial conditions. We try to balance the bias of the estimator in a simulation run by imposing a bias in the opposite direction in a companion run by suitably setting its initial conditions. We present analytical results for the bias of our estimator for AR(1) and MMs processes. We suggest making independent replications of the pairs of runs to construct a confidence interval for the mean response. We present some empirical results about the coverages and precisions of the confidence intervals. The results suggest that the idea of balancing a bias with a bias in the opposite direction is promising. 1
A Methodology for the Determination of Data Truncation Point for Initialisation Bias Reduction in Computer Simulation Output
, 1991
"... We present a new methodology for detecting when the steady state behaviour of a discreteevent computer simulation has been approached after starting from a nontypical initial state. An implementation of this methodology is given which is most powerful for an initialisation transient of exponential ..."
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We present a new methodology for detecting when the steady state behaviour of a discreteevent computer simulation has been approached after starting from a nontypical initial state. An implementation of this methodology is given which is most powerful for an initialisation transient of exponential form. Keywords: computer simulation, initialization bias 1 Introduction In computer simulation studies an estimate is often required for the steadystate mean of some quantity of interest. For each computer run the model must be initialised to some known state. In queueing systems, for example, the "emptyand idle" state is commonly used because of its convenience. If this initial state is not chosen at random from the steadystate distribution of the system under simulation (which in general is unknown) then the inclusion of early observations in an estimator can lead to a systematic bias in that estimator known as initialisation bias. One common approach is to wait for the simulation t...
Technical Report
, 1988
"... Literature over the past ten years has illustrated the ramifications of statistical bias due to the initial state of a system. Simply, long term averages will be tainted by the observations which occur while the statistic approaches steady state. Determining realistic techniques for estimating the ..."
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Literature over the past ten years has illustrated the ramifications of statistical bias due to the initial state of a system. Simply, long term averages will be tainted by the observations which occur while the statistic approaches steady state. Determining realistic techniques for estimating the length of the transient period is a significant problem, particularly in systems with which there is no experience. This study focuses on the comparison and evaluation of several techniques for determining the length of transient periods. Markovian queues are used as the testbed for these techniques. The algorithms are described, applied, and evaluated. Conclusions based on the results are presented, as well as feasible alternatives and extensions for later work. 2. Introduction In using simulations of a stochastic system, the question of statistical bias due to system initialization has been significant in many works. Consider an arbitrary system in which some measure of the performance i...