Efficient MCMC estimation of discrete distributions

In this paper we propose an efficient Markov chain Monte Carlo (MCMC) method for estimation of discrete distributions by solving an appropriate system of linear equations. We call the estimator the equation-solving estimator. Our numerical results show that the new estimator makes significant improvements over the conventional frequency MCMC estimator in terms of accuracy of the estimates. The new estimator can be used in Bayesian model comparison problems.