Journal ArticleDOI
Sensitivity analysis from sample paths using likelihoods
Philip Heidelberger,Don Towsley +1 more
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In this article, the authors modify the likelihood-based method for obtaining derivatives with respect to the rate of a Poisson process to that it is not necessary to know the exact value of that rate.Abstract:
We modify the likelihood-based method for obtaining derivatives with respect to the rate of a Poisson process to that it is not necessary to know the exact value of that rate. This type of modification is necessary if the method is to be used on a sample path from a real system. The method is also applicable to simulation studies of certain real time control policies and may be useful in trace driven simulations. The modification to the likelihood estimator is simply to use the value of the Poisson rate estimated during the sample interval. For regenerative systems, this produces a strongly consistent, asymptotically normal and asymptotically unbiased estimate of the derivative. The strong law and central limit theorem are generalized to the case of estimating a derivative with respect to an unknown parameter from the exponential class of probability density functions. Numerical results for the M/M/1 queue illustrate little difference between the estimates for the derivative of the expected delay with respect to arrival rate obtained when the arrival rate is known and unknown. However, both estimates are highly biased for small sample sizes. This bias can be reduced by jackknifing.read more
Citations
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Journal ArticleDOI
Convergence of Probability Measures
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
Proceedings ArticleDOI
An overview of derivative estimation
TL;DR: The author explains the main techniques for estimating derivatives by simulation and surveys the most recent developments in that area, including perturbation analysis, likelihood ratios, weak derivatives, finite differences, and many of their variants.
Journal ArticleDOI
Distributed routing with on-line marginal delay estimation
TL;DR: A procedure is presented for estimating online marginal packet delays through links with respect to link flows without making the standard assumptions (exponentially distributed packet lengths, Poisson arrival processes) based on a technique known as perturbation analysis.
Proceedings ArticleDOI
Imbedding gradient estimators in load balancing algorithms
TL;DR: The results indicate that the estimators are accurate, the algorithm chooses good thresholds, and the resultant response time of jobs is near optimal.
Journal ArticleDOI
On sampling controlled stochastic approximation
Paul Dupuis,Rahul Simha +1 more
TL;DR: The authors address the growth rate required of the number of samples and prove a general convergence theorem for the proposed stochastic approximation method, and derive a sampling controlled version of the classic Robbins-Munro algorithm.
References
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Book
Convergence of Probability Measures
TL;DR: Weak Convergence in Metric Spaces as discussed by the authors is one of the most common modes of convergence in metric spaces, and it can be seen as a form of weak convergence in metric space.
Journal ArticleDOI
Convergence of Probability Measures
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
Book
A first course in stochastic processes
Samuel Karlin,Howard M. Taylor +1 more
TL;DR: In this paper, the Basic Limit Theorem of Markov Chains and its applications are discussed and examples of continuous time Markov chains are presented. But they do not cover the application of continuous-time Markov chain in matrix analysis.
Book
Introduction to Mathematical Statistics
TL;DR: In this article, the authors present a list of common distributions of probability and distribution of likelihood for Bayesian models. But they do not discuss the relation between distributions and normal models.
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