ach is used to generate an estimate <span class="math inline">\(\hat{\sigma}^{\textrm{boot}(n)}.\)</span> The final estimate is <span class="math display">\[
\hat{\sigma} = \frac{1}{N} \sum_{n = 1}^N \hat{\sigma}^{\textrm{boot}(n)}.
\]</span> The same would be done to estimate a predictive quantity <span class="math inline">\(\tilde{y}\)</span> for as yet unseen data. <span class="math display">\[
\hat{\tilde{y}} = \frac{1}{N} \sum_{n = 1}^N
\hat{\tilde{y}}^{\textrm{boot}(n)}.
\]</span> For discrete paramet