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 twodimensional 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:
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Whoa… that’s some serious overplotting 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?