Lets say I have $n$ posterior samples of $\theta_1$ and $\theta_2$. I suppose that any region $R$ which contains exactly $(1-\alpha)n$ of the points will be an approximate $(1-\alpha)\times100$ credible region for $(\theta_1, \theta_2)$. Can anybody make any suggestions, or point me to some literature for methods of constructing a good credible region $R$?
If it matters, this is a simulation study and I would like to evaluate the frequentist coverage of the region $R$ (I know there is no guarantee that the coverage will be nominal).
Off the top of my head, I can imagine an algorithm which checks all possible rectangular regions and gives some criteria for choosing one (smallest area?). It seems to me that we should be able to do better without enforcing a rectangular region. Any other method I can think of would use KDE, which intuitively bothers me since it could be sensitive to the choice of bandwith.