Posterior rank distribution ($r_i=1+{\sum }_{k\ne i}1\{{\lambda }_k>{\lambda }_i\}$)

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.