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I thought of a procedure to generate high probability density regions with probability $1-\alpha$ from $n$ MCMC draws:

  1. Find the $\lfloor(1-\alpha)\cdot n\rfloor$ draws with the largest probability density;
  2. Take the confidence hull of these draws as an approximate HPD region.

Is this procedure correct? I believe it only works when the distribution is convex (or maybe log-convex, I'm not sure). I think this is a more flexible approach than using Mahalanobis distance, since the resulting region is convex but not ellipsoidal, and requires less tuning than kernel density based methods.

Thanks in advance!

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  • $\begingroup$ How many dimensions are we talking here? :) $\endgroup$
    – usεr11852
    Commented Jan 26, 2022 at 3:02
  • $\begingroup$ @usεr11852 I was thinking 2-3 dimensions. Would it fail in high dimensions? KDE would fail there too due to the curse of dimensionality, right? $\endgroup$
    – PedroSebe
    Commented Jan 26, 2022 at 3:26
  • $\begingroup$ Yes, my worry was this would be used in some with 10+ dimensions where I would expect it to down-right fail. $\endgroup$
    – usεr11852
    Commented Jan 26, 2022 at 10:05

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