Before revision: 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.
After revision: We explore the possibility of combining Markov chain Monte Carlo (MCMC) estimates of rare event probabilities, and we make three contributions. First, we prove there is a unique splitting method providing asymptotically consistent estimates when combined with MCMC.