Simulation from a target distribution based on discretization and
weighting
S. Malefaki and G. Iliopoulos
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.
Key words and phrases: discretization;
properly weighted samples; Markov chain Monte Carlo; autocorrelations.