1,720,994 research outputs found
Analysis of simulation output by resampling
No full textBootstrap resampling is an extremely practical and effective way of studying the distributional properties of simulation output when this is subject to random variation. The purpose of this paper is to show that many problems of sensitivity analysis (SA) and validation can be very simply handled by this method. We consider classical non-parametric version of the bootstrap and show that it can be applied in a natural way in simulation studies without becoming immersed in complicated statistical methodology. The main message of the paper is that the bootstrap method should be the statistical method of first resort in SA and validation studies
Analysis of Simulation Experiments by Bootstrap Resampling
No full textThis tutorial considers some very general procedures for analysing the results of a simulation experiment using bootstrap resampling. Bootstrapping has come to be recognised in statistics as being far ranging and effective. However it is not so well known in simulation despite being ideally suited for use in such a context. We discuss aspects ranging from the elementary to the advanced. We describe the rationale and the simple steps needed to implement bootstrapping in (i) estimation of the distributional properties of the output and its dependence on factors of interest; (ii) model fitting; (iii) model selection; (iv) model validation; (v) sensitivity analysi
Threshold estimation in the log-gamma model
No full textThe three-parameter log-gamma distribution is a versatile lifetime model. However, it has a quite unusual property that allows it to be used as a potential threshold model: namely, that though it is not left-limited in general, it includes the shifted exponential as a special case. Thus, it is a useful bridge between skewed models that are not explicitly left-limited, on the one hand, and a true threshold model on the other. It is shown that the likelihood always has a local maximum corresponding to the exponential model, even when this is not the true model, so that the usual maximum likelihood (ML) estimator is unsatisfactory. An estimator obtained by maximising a certain spacing-modified likelihood is proposed that does not suffer from this problem. Its distributional properties are derived showing it to be as efficient as ML when this does work and moreover showing the estimators of shape and location to be hyper-efficient when the exponential model is the true model. Simulation results and three numerical examples are given contrasting the behaviour of the proposed estimator with the ML estimator
Optimal design of simulation experiments with nearly saturated queues
Full text linkSimulation Models;Interpolation;Queueing Network;Extrapolation
Prior and candidate models in the Bayesian analysis of finite mixtures
No full textThis paper discusses the problem of fitting mixture models to input data. When an input stream is an amalgam of data from different sources then such mixture models must be used if the true nature of the data is to be properly represented. A key problem is then to identify the different components of such a mixture, and in particular to determine how many components there are. This is known to be a non-regular/non-standard problem in the statistical sense and is technically notoriously difficult to handle properly using classical inferential methods. We discuss a Bayesian approach and show that there is a theoretical basis why this approach might overcome the problem. We describe the Bayesian approach explicitly and give examples showing its application
Calculation of confidence Intervals for simulation output
No full textThis article is concerned with the calculation of confidence intervals for simulation output that is dependent on two sources of variability. One, referred to as <i>simulation variability</i>, arises from the use of random numbers in the simulation itself; and the other, referred to as <i>parameter variability</i>, arises when the input parameters are unknown and have to be estimated from observed data. Three approaches to the calculation of confidence intervals are presented--the traditional asymptotic normality theory approach, a bootstrap approach and a new method which produces a conservative approximation based on performing just two simulation runs at carefully selected parameter settings. It is demonstrated that the traditional and bootstrap approaches provide similar degrees of accuracy and that whilst the new method may sometimes be very conservative, it can be calculated in a small fraction of the computational time of the exact methods.<br/
Analysis of distributions in factorial experiments
No full textThe Cramer-von Mises statistic provides a useful goodness of fit test of whether a random sample has been drawn from some given null distribution. Its use in comparing several samples has also been studied, but not systematically. We show that the statistic is capable of significant generalization. In particular we consider the comparison of the distributions of observations arising from factorial experiments. Provided that observations are replicated, we show that our generalization yields a test statistic capable of decomposition like the sum of squares used in ANOVA. The statistic is calculated using ranked data rather than original observations. We give the asymptotic theory. Unlike ANOVA, the asymptotic distributional properties of the statistic can be obtained without the assumption of normality. Further, the statistic enables differences in distribution other than the mean to be detected. Because it is distribution free, Monte-Carlo sampling can be used to directly generate arbitrarily accurate critical test null values in online analysis irrespective of sample size. The statistic is thus easy to implement in practice. Its use is illustrated with an example based on a man-in-the-loop simulation trial where operators carried out self assessment of the workload that they experienced under different operating conditions
A fast distance based approach for determining the number of components in mixtures
No full textThe authors propose a procedure for determining the unknown number of components in mixtures by generalizing a Bayesian testing method proposed by Mengersen & Robert (1996). The testing criterion they propose involves a Kullback-Leibler distance, which may be weighted or not. They give explicit formulas for the weighted distance for a number of mixture distributions and propose a stepwise testing procedure to select the minimum number of components adequate for the data. Their procedure, which is implemented using the BUGS software, exploits a fast collapsing approach which accelerates the search for the minimum number of components by avoiding full refitting at each step. The performance of their method is compared, using both distances, to the Bayes factor approach
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