Monte Carlo Statistical Methods (Springer Texts in Statistics)
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Simulation and the Monte Carlo Method (Wiley Series in Probability and Statistics)
Simulation and the Monte Carlo Method (Wiley Series in Probability and Statistics)
Approximate zero-variance simulation
Proceedings of the 40th Conference on Winter Simulation
Efficient Monte Carlo simulation via the generalized splitting method
Statistics and Computing
Markov chain importance sampling with applications to rare event probability estimation
Statistics and Computing
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We propose a new importance sampling method that constructs an importance sampling density which approximates the zero-variance sampling density nonparametrically as follows. In a first stage, it generates a sample (possibly approximately) from the zero-variance density using, for example, Markov chain Monte Carlo methodology. In a second stage, the method constructs a kernel density estimator of the zero-variance density based on the sample in the first stage. The most important aspect of the method is that, unlike other kernel estimation methods, the kernel of the estimator is defined as the one-step transition density of a Markov chain whose stationary distribution is the zero-variance one. We give examples where this one-step transition density is available analytically and provide numerical illustrations in which the method performs very well.