On convergence of importance sampling and other properly weighted samples to the target distribution

Details On convergence of importance sampling and other properly weighted samples to the target distribution On convergence of importance sampling and other properly weighted samples to the target distribution

2005-05-03

arxiv.org/abs/math/0505045v2

Mathematics

Statistics Theory

15 pagers, 1 figure

Scientific paper

We consider importance sampling as well as other properly weighted samples with respect to a target distribution $\pi$ from a different point of view. By considering the associated weights as sojourn times until the next jump, we define appropriate jump processes. When the original sample sequence forms an ergodic Markov chain, the associated jump process is an ergodic semi--Markov process with stationary distribution $\pi$. Hence, the type of convergence of properly weighted samples may be stronger than that of weighted means. In particular, when the samples are independent and the mean weight is bounded above, we describe a slight modification in order to achieve exact (weighted) samples from the target distribution.

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