47,717 research outputs found
Split Sampling: Expectations, Normalisation and Rare Events
In this paper we develop a methodology that we call split sampling methods to
estimate high dimensional expectations and rare event probabilities. Split
sampling uses an auxiliary variable MCMC simulation and expresses the
expectation of interest as an integrated set of rare event probabilities. We
derive our estimator from a Rao-Blackwellised estimate of a marginal auxiliary
variable distribution. We illustrate our method with two applications. First,
we compute a shortest network path rare event probability and compare our
method to estimation to a cross entropy approach. Then, we compute a
normalisation constant of a high dimensional mixture of Gaussians and compare
our estimate to one based on nested sampling. We discuss the relationship
between our method and other alternatives such as the product of conditional
probability estimator and importance sampling. The methods developed here are
available in the R package: SplitSampling
A subset multicanonical Monte Carlo method for simulating rare failure events
Estimating failure probabilities of engineering systems is an important
problem in many engineering fields. In this work we consider such problems
where the failure probability is extremely small (e.g ). In this
case, standard Monte Carlo methods are not feasible due to the extraordinarily
large number of samples required. To address these problems, we propose an
algorithm that combines the main ideas of two very powerful failure probability
estimation approaches: the subset simulation (SS) and the multicanonical Monte
Carlo (MMC) methods. Unlike the standard MMC which samples in the entire domain
of the input parameter in each iteration, the proposed subset MMC algorithm
adaptively performs MMC simulations in a subset of the state space and thus
improves the sampling efficiency. With numerical examples we demonstrate that
the proposed method is significantly more efficient than both of the SS and the
MMC methods. Moreover, the proposed algorithm can reconstruct the complete
distribution function of the parameter of interest and thus can provide more
information than just the failure probabilities of the systems
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