= Posterior rank distribution
{title2=$r_i=1+\sum_{k\ne i}\mathbf1\{\lambda_k>\lambda_i\}$}
For continuously distributed uncertain quantities, define rank one to be the largest. A joint <posterior distribution> induces a discrete distribution on each quantity's rank. Estimate it by ranking the whole vector in each joint draw and averaging rank indicators; the probability of rank one is the probability of being largest. Ranking <posterior means> does not recover this uncertainty. The joint draws must preserve any posterior dependence, and tie conventions must be specified for models with atoms.
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