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arXiv · 0710.3684

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

Mylène Bédard
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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.

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Mylène Bédard. 2007-10-19. Weak convergence of Metropolis algorithms for non-i.i.d. target distributions. https://doi.org/10.1214/105051607000000096

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