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One main limitation of the existing optimal scaling results forMetropolis--Hastings algorithms is that the assumptions on the targetdistribution are unrealistic. In this paper, we consider optimal scaling ofrandom-walk Metropolis algorithms on general target distributions in highdimensions arising from practical MCMC models from Bayesian statistics. Foroptimal scaling by maximizing expected squared jumping distance (ESJD), we showthe asymptotically optimal acceptance rate $0.234$ can be obtained undergeneral realistic sufficient conditions on the target distribution. The newsufficient conditions are easy to be verified and may hold for some generalclasses of MCMC models arising from Bayesian statistics applications, whichsubstantially generalize the product i.i.d. condition required in most existingliterature of optimal scaling. Furthermore, we show one-dimensional diffusionlimits can be obtained under slightly stronger conditions, which still allowdependent coordinates of the target distribution. We also connect the newdiffusion limit results to complexity bounds of Metropolis algorithms in highdimensions.

Optimal Scaling of Random-Walk Metropolis Algorithms on General Target Distributions