How to calculate a 95 credible region for a 2D joint distribution?
If you are interested in finding a pair x_1, x_2 of real numbers such that
P(X_1<=x_1, X_2<=x_2) = 0.95 and your distribution is continuous then there will be infinitely many of these pairs. You might be better of just fixing one of them and then finding the other
Suppose we have a joint distribution p(x_1,x_2), and we know x_1,x_2,p. Both are discrete, (x_1,x_2) is scatter, its contour could be drawn, marginal as well. I would like to show the area of 95% quantile (a scale of 95% data will be contained) of the joint distribution, how can I do that?