  Parameter ensembles or sets of point estimates constitute one of the
cornerstones of modern statistical practice. This is especially the case in
Bayesian hierarchical models, where different decision-theoretic frameworks can
be deployed to summarize such parameter ensembles. The estimation of these
parameter ensembles may thus substantially vary depending on which inferential
goals are prioritised by the modeller. In this note, we consider the problem of
classifying the elements of a parameter ensemble above or below a given
threshold. Two threshold classification losses (TCLs) --weighted and
unweighted-- are formulated. The weighted TCL can be used to emphasize the
estimation of false positives over false negatives or the converse. We prove
that the weighted and unweighted TCLs are optimized by the ensembles of
unit-specific posterior quantiles and posterior medians, respectively. In
addition, we relate these classification loss functions on parameter ensembles
to the concepts of posterior sensitivity and specificity. Finally, we find some
relationships between the unweighted TCL and the absolute value loss, which
explain why both functions are minimized by posterior medians.
