On convergence of properly weighted samples
to the target distribution
Sonia Malefaki and George Iliopoulos
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 $\pi$.
In this respect, properly weighted samples behave very similarly to standard
Markov chain Monte Carlo (MCMC) schemes in that they exhibit convergence to the
target distribution as well. Indeed, some standard MCMC procedures like the
Metropolis--
Key words and phrases: Importance
sampling, properly weighted samples, Markov chain