How to calculate a 95 credible region for a 2D joint distribution?
As the other points out, there are infinitely many solutions to this problem. A practical one is to find the approximate center of the point cloud and extend a circle from there until it contains approximately 95% of the data. Then, find the convex hull of the selected points and compute its area.
Of course, this will only work if the data is sort of concentrated in a single area. This won't work if there are several clusters.
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?