Simulation from a Target Distribution Based on Discretization and Weighting

We present a simulation method which is based on discretization of the state space of the target distribution (or some of its components) followed by proper weighting of the simulated output. The method can be used in order to simplify certain Monte Carlo and Markov chain Monte Carlo algorithms. Its main advantage is that the autocorrelations of the weighted output almost vanish and therefore standard methods for iid samples can be used for estimating the Monte Carlo standard errors. We illustrate the method via toy examples as well as the well-known dugongs and Challenger datasets.