I'm running an MCMC scheme defined in A tutorial on adaptive MCMC. Christophe Andrieu·Johannes Thoms. Stat Comput (2008) 18: 343–373DOI 10.1007/s11222-008-9110-y.
They say the optimal scaling factor for the covariance matrix is $(2.38)^2/n_x$, where $n_x$ is the number of parameters I have.
Originally I had an extra layer of adaptivity to change this scaling parameter to keep it at around 25%, but it seems as though this isn't allowed. My question is whether or not I'm allowed to use a much much smaller scaling factor, as currently my acceptance ratio is converging to 0. Or is it likely I've done something else wrong if the acceptance ratio is very low? In my case, $n_x = 8$. I'm also using simulated data at the moment, so I don't have issues with the model not being correct for the data.
