We study an initial transient deletion rule proposed by Glynn and Iglehart. We argue that it has desirable properties both from a theoretical and practical standpoint; we discuss its bias reducing properties, and its use both in the single replication setting and in the multiple replications / parallel processing context.
Simulation-based ordinal optimization has frequently relied on large deviations analysis as a theoretical device for arguing that it is computationally easier to identify the best system out of d alternatives than to estimate the actual performance of a given design. In this paper, we argue that practical implementation of these large deviations-based methods need to estimate the underlying large deviations rate functions of the competing designs from the samples generated. Because such rate functions are difficult to estimate accurately (due to the heavy tails that naturally arise in this setting), the probability of mis-estimation will generally dominate the underlying large deviations probability, making it difficult to build reliable algorithms that are supported theoretically through large deviations analysis. However, when we justify ordinal optimization algorithms on the basis of guaranteed finite sample bounds (as can be done when the associated random variables are bounded), we show that satisfactory and practically implementable algorithms can be designed.
Consider a simulation estimator α(c) based on expending c units of computer time, to estimate a quantity α. One measure of efficiency is to attempt to minimize P (|α(c) − α| > ) for large c. This helps identify estimators with less likelihood of witnessing large deviations. In this article we establish an exact asymptotic for this probability when the underlying samples are independent and a weaker large deviations result under more general dependencies amongst the underlying samples.
This tutorial is intended to provide an overview of the key algorithms that are used to simulate sample paths of diffusion processes, as well as to offer an understanding of their fundamental approximation properties.
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