ared error</em> as <span class="math display">\[
\textrm{sq-err} = \left( \hat{\theta} - \theta \right)^2.
\]</span> <span class="citation" data-cites="GneitingRaftery:2007">Gneiting and Raftery (<a href="#ref-GneitingRaftery:2007" role="doc-biblioref">2007</a>)</span> provide a thorough overview of such scoring rules and their properties.</p>
<p>Bayesian posterior means minimize expected square error, whereas posterior medians minimize expected absolute error. Estimates based on modes rather than probabili