We explore the possibility of combining Markov chain Monte Carlo (MCMC) with the rare event sampling approach known as ``splitting and killing. " First, we prove there is a unique splitting method providing asymptotically consistent estimates when combined with MCMC. This splitting method, called weighted ensemble, has been known since 1997, yet its advantages over MCMC have not yet been precisely quantified. Our second contribution, therefore, is to clarify weighted ensemble's properties by providing a lower bound on the asymptotic variance of the method 's estimates. We give a constructive proof and numerical examples to show  weighted ensemble can approach this optimal variance bound, in many cases reducing the variance of MCMC estimates by multiple orders of magnitude.
We explore whether splitting and killing methods can improve the accuracy of Markov chain Monte Carlo (MCMC) estimates of rare event probabilities, and we make three contributions. First, we prove that "weighted ensemble" is the only splitting and killing method that provides asymptotically consistent estimates when combined with MCMC. Second, we prove a lower bound on the asymptotic variance of weighted ensemble 's estimates. Third, we give a constructive proof and numerical examples to show that weighted ensemble can approach this optimal variance bound, in many cases reducing the variance of MCMC estimates by multiple orders of magnitude.
R
the possibility of combining
whether splitting and killing methods can improve the accuracy of
R
with the rare event sampling approach known as ``splitting and killing. "
estimates of rare event probabilities, and we make three contributions.
R
there is a unique splitting method providing
that "weighted ensemble" is the only splitting and killing method that provides
R
This splitting method, called weighted ensemble, has been known since 1997, yet its advantages over MCMC have not yet been precisely quantified. Our second contribution, therefore, is to clarify weighted ensemble's properties by providing
Second, we prove
R
the method
weighted ensemble
R
We
Third, we
A
that