 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 probability, such as (penalized) maximum likelihood estimates or maximum a posterior estimates, do not have these properties.</p>
</section>
<section id="predictive-estimates" class="level3 unnumbered">
<h3 class="unnumbered anchored" data-anchor-id="predictive-estimates">Predictive esti