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Optimal scaling of the random walk Metropolis on elliptically symmetric unimodal targets

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Figure

Figure 1. Plots for a Gaussian target (left) and the Gaussian mixture target of (both at11) with pd = 1/d2 (right), d = 10 and with a Gaussian jump proposal
Figure 2. Plots of the optimal EARproposal. The horizontal dotted line approximates the apparent asymptotically optimal acceptance rate of0 ˆα against dimension for example targets 1–4 using a Gaussian jump.234 in the first two plots and 0.10 and 0.06 in the third and fourth plots, respectively.
Figure 3. Plots of the optimal EAR ˆα against dimension for example targets 6–8 using a Gaussian jumpproposal
Figure 4. Plots of log λˆ against logd for target examples 1–4. Optimal values predicted using Corollary 4appear as dotted lines.

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