</span> and <span class="arithmatex">\(\hat\Sigma^{\text{new}}\)</span>, and link them back with <span class="arithmatex">\(\pi_k\)</span>, <span class="arithmatex">\(\hat\mu_k\)</span> and <span class="arithmatex">\(\hat\Sigma\)</span> estimated from original training data.</p>
<p>First, <span class="arithmatex">\(\pi_k^{\text{new}} = \pi_k\)</span> for <span class="arithmatex">\(k=1,...,K\)</span> since the training sample classification does not change.</p>
<p>Second, by definition of <span class="arithm