Monte Carlo Integration Using Importance Sampling and Gibbs Sampling

Wolfgang Hörmann and Josef Leydold


To evaluate the expectation of a simple function with respect to a complicated multivariate density Monte Carlo integration has become the main technique. Gibbs sampling and importance sampling are the most popular methods for this task. In this contribution we propose a new simple general purpose importance sampling procedure. In a simulation study we compare the performance of this method with the performance of Gibbs sampling and of importance sampling using a vector of independent variates. It turns out that the new procedure is much better than independent importance sampling; up to dimension five it is also better than Gibbs sampling. The simulation results indicate that for higher dimensions Gibbs sampling is superior.

Mathematics Subject Classification: 65C05 (Monte Carlo Methods)

General Terms: Algorithms

Key Words: Markov chain Monte Carlo method, Gibbs sampling, importance sampling

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