Weak convergence of Metropolis algorithms for non-i.i.d. target distributions

Preprint

19 October 2007

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.0710.3684

Abstract

In this paper, we shall optimize the efficiency of Metropolis algorithms for multidimensional target distributions with scaling terms possibly depending on the dimension. We propose a method for determining the appropriate form for the scaling of the proposal distribution as a function of the dimension, which leads to the proof of an asymptotic diffusion theorem. We show that when there does not exist any component with a scaling term significantly smaller than the others, the asymptotically optimal acceptance rate is the well-known 0.234.

Keywords

METROPOLIS ALGORITHMS
TARGET DISTRIBUTIONS
WEAK CONVERGENCE
SCALING TERM
EFFICIENCY
DIFFUSION
OPTIMIZE
I.I.D

All Related Versions

Version 1, 2007-10-19, ArXiv
Published version: The Annals of Applied Probability, 17 (4), 1222.

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