Monte Carlo Integration Using Importance Sampling and Gibbs Sampling
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)
Markov chain Monte Carlo method,