Correlation between variables in posterior

Questions
1

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?

Thank you!

2

Yes.

Yes.

Yes, although I would hesitate to refer to these as “correlations between estimated variables”, because that would suggest (to me) that you are talking about associations between measurements. Instead, I would describe them as dependencies between credible values of model parameters. These dependencies could be brought about by associations in the observed data, but could also be brought about by your priors, the structure of the model, or any combination of these ingredients.

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3

Thank you for the timely and excellent feedback!