Rare-Event Simulation

# Rare-Event Simulation - Rare-Event Simulation Splitting for...

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Rare-Event Simulation Splitting for Variance Reduction IE 680, Spring 2007 Bryan Pearce

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What is a Rare Event? Ω A B
Formal Problem Definition { } { } { } [ ] A B B 1 A 0 is estimate to like would that we measure y probabilit then the " reached, is state first time the " : 0 inf and reached" is state first time the " and : 0 inf If . \ x state initial an with and event), rare the from (far and event) rare (the subsets disjoint with the , space state on the chain Markov time - discrete a define 0 Let τ γ < = = = - P B B X j A A X A X j B A B ,j X j j j j [ ] [ ] ( 29 0. as to increases ˆ Var ˆ estimator MC simple The 2 1 = n n RE

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Splitting: the beginning Importance function h Measures “how close” a state is to the rare event Divide the intermediary state space into m ‘levels’ according to the thresholds l 0 , l 1 , …, l m
h(x) = l 0 = l 1 = l 2 = l 3 = l m = l

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{ } { } ( 29 ( 29 events rare' so not ' of series A ... 0 levels - sub specified user by subdivided is interval this 0 on values have will or in not states All ) ( : 0 ) ( : : : space state the of ordering an allows function Importance specified - user A 1 0 l
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Rare-Event Simulation - Rare-Event Simulation Splitting for...

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