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Target distribution is multimodal, 24 dimensions, continuous state space. For MCMC integration (MH sampler) I use a manually tuned proposal distribution.

When I measure the convergence rate numerically I observe only a polynomial convergence rate.

I have a complete freedom of choice for the proposal distribution. Are there practically useful conditions to quickly check if a particular proposal distribution leads to the geometric convergence rate?

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I guess this is a difficult topic. Maybe this recent manuscript could be helpful

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Thank you for the suggestion. An interesting reading indeed. The only question I have is that it seems like the transformation can help with heavy tails. However it is not clear for me how it helps with reachability of distinct modes. Thanks, Anton –  Anton Dec 7 '12 at 11:21
    
@Anton. That is definitely an interesting (and not easy) question. It is not clear to me either. –  an12 Dec 8 '12 at 5:05

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