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The problem is that I have a Gibbs-Sampler where one of the parameters has to be sampled via a Metropolis-Step from the respective FCD. I have problems finding a suitable scale for the Gaussian proposal density.

In the Paper Hierarchical Bayesian modeling of random and residual variance–covariance matrices in bivariate mixed effects models, I found the following:

[...] the proposal density is Gaussian with mean equal to the mode of the FCD function and a variance equal to the negative of the inverse Hessian of the FCD function evaluated at the previously sampled value [...].

Question: Will this give me valid samples from the correct posterior distribution?

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It will give valid samples, provided you include the correct Hastings factor in the acceptance ratio. But using the inverse Hessian directly as the variance can be dangerous, and some additional corrections are recommended. For more details, see the paper Hessian-based Markov Chain Monte-Carlo Algorithms. The algorithm presented there is a bit different than the one you described, but many of the same considerations apply.

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