ass="math inline">\(K\)</span> can be finite (e.g., number of Bernoulli experiments) or infinite (count data). We let also <span class="math inline">\(\pi_{ijk} = \Pr(Y_{ij} = k)\)</span>, <span class="math inline">\(k = 1, \ldots, K\)</span>. A scoring rule <span class="math inline">\(R(\pi_{ij}, \{Y_{ij} = k\})\)</span> is a function that assigns a score for the forecast <span class="math inline">\(\{\pi_{ijk}; k = 1, \ldots, K\}\)</span> upon observing the outcome <span class="math inline">\(\{Y_{ij} = k