Making a slight digression from last month’s Probable Points and Credible Intervals here is how to summarize a 2D posterior density using a highest density ellipse. This is a straight forward extension of the highest density interval to the situation where you have a two-dimensional posterior (say, represented as a two column matrix of
samples) and you want to visualize what region, containing a given proportion of the probability, that has the most probable parameter combinations. So let’s first have a look at a fictional 2D posterior by using a simple scatter plot:
Whoa… that’s some serious over-plotting and it’s hard to see what’s going on. Sure, the bulk of the posterior is somewhere in that black hole, but where exactly and how much of it?