Importance Sampling and the Cyclic Approach

The method of importance sampling is widely used for efficient rare-event simulation of stochastic systems. This method involves simulating the system under a new distribution that accentuates the probability along the most likely paths to the rare event. Traditionally, insights from large deviation...

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Vydané v:Operations research Ročník 49; číslo 6; s. 900 - 912
Hlavný autor: Juneja, Sandeep
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Linthicum INFORMS 01.11.2001
Institute for Operations Research and the Management Sciences
Predmet:
Acoustical engineering
Computer networks
Engineering firms
Error rates
Estimators
Gas stations
Markov chains
Markov processes
Network servers
Operations research
Planning
Probability
Random variables
Random walk
Ratios
Sampling (Sound engineering)
Simulation
Simulation: importance sampling
Stochastic analysis
Stochastic models
Stochastic processes
Studies
United States
ISSN:0030-364X, 1526-5463
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Shrnutí:The method of importance sampling is widely used for efficient rare-event simulation of stochastic systems. This method involves simulating the system under a new distribution that accentuates the probability along the most likely paths to the rare event. Traditionally, insights from large deviations theory are used to identify the distribution emphasizing these most likely paths. In this paper we develop an intuitive cyclic approach for selecting such a distribution. The key idea is to select a distribution under which the event of interest is no longer rare and the probability of occurrence of a cycle in any sample path remains equal to the original probability of that cycle. We show that only an exponentially twisted distribution can satisfy this equiprobable cycle condition. Using this approach we provide an elementary derivation of the asymptotically optimal change of measure for level crossing probability for Markov-additive processes. To demonstrate its ease of use for more complex stochastic systems, we apply it to determine the asymptotically optimal change of measure for estimating buffer overflow probability of a single-server queue subject to server interruptions.
Bibliografia:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0030-364X
1526-5463
DOI:10.1287/opre.49.6.900.10016