u_k^T\Sigma^{-1}\mu_k + \log \pi_k
\end{equation}\]</div>
<p>where <span class="arithmatex">\(\pi_k\)</span> is the <em>prior probability</em> of class <span class="arithmatex">\(k\)</span>. </p>
<p>Parameters are estimated as </p>
<div class="arithmatex">\[\begin{eqnarray}
    \hat\pi_k &amp;=&amp; \frac{n_k}{n}\non\\
    \hat\mu_k &amp;=&amp; \frac{1}{n_k}\sum_{y_i=k}x_i\non\\
    \hat\Sigma &amp;=&amp;\frac{1}{n-k}\sum_{k=1}^K\sum_{y_i=k}(x_i-\hat\mu_k)(x_i-\hat\mu_k)^T.\non
\end{eqnarray}\]</div>
<p>The