Optimal scaling of Metropolis algorithms:heading toward general target distributions

摘要

The authors provide an overview of optimal scaling results for the Metropolis algorithm withGaussian proposal distribution. They address in more depth the case of high-dimensional target distribu-tions formed of independent, but not identically distributed components. They attempt to give an intuitiveexplanation as to why the well-known optimal acceptance rate of 0.234 is not always suitable. They showhow to find the asymptotically optimal acceptance rate when needed, and they explain why it is sometimesnecessary to turn to inhomogeneous proposal distributions. Their results are illustrated with a simple ex-ample.