I am implementing an inference scheme in which the mean value is given by a very complex scattering model, which depends on 8 different physical variables. The estimation run smoothly with uniform priors, but since I have a single observation and a noisy observation model, it is expected that several combinations of the physical variables can explain the observation. I want to estimate areas of the multidimensional posterior for which there a relatively large probability given the observation. Therefore, I need access to the complete posterior distribution.
Maybe is a simple issue, but can I use the chains to estimate the full posterior? Are every index of the chain a sample from the full posterior distribution? And if this is true, can I use the correlations between chains to compute correlations between estimated variables?