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It looks like you are using the inverse of the Hessian at the posterior mode as an (initial) proposal covariance. Have you tried scaling this, as in Roberts and Rosenthal, "Examples of adaptive MCMC" (2009)? Not sure if this will help if you're modifying the proposal later. Also, it looks like you can evaluate the Hessian of your posterior at an arbitrary point, not just the mode. Have you considered using a Hessian-exploiting version of Metropolis-Hastings, like stochastic Newton (e.g. arXiv:stat/1502.02008)?
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Dec 3, 2015