Rao-Blackwellisation of sampling schemes. (English) Zbl 0866.62024

Casella, George; Robert, Christian P.

Biometrika 83, No. 1, 81-94 (1996).

Summary: This paper proposes a post-simulation improvement for two common Monte Carlo methods, the Accept-Reject and Metropolis algorithms. The improvement is based on a Rao-Blackwellisation method that integrates over the uniform random variables involved in the algorithms, and thus post-processes the standard estimators. We show how the Rao-Blackwellised versions of these algorithms can be implemented and, through examples, illustrate the improvement in variance brought by these new procedures. We also compare the improved version of the Metropolis algorithm with ordinary and Rao-Blackwellised importance sampling procedures for independent and general Metropolis set-ups.

MSC:

62G99	Nonparametric inference
62D05	Sampling theory, sample surveys
62G05	Nonparametric estimation

Keywords:

accept-reject; Gibbs sampling; polynomial computing time; post-simulation improvement; Monte Carlo methods; Metropolis algorithms; Rao-Blackwellisation method; importance sampling