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?