ction level3 unnumbered">
<h3>Mixtures with Unidentifiable Components</h3>
<p>As an example, consider the normal mixture from the previous section,
which provides an exchangeable prior on the pairs of parameters
<span class="math inline">\((\mu_1, \sigma_1)\)</span> and <span class="math inline">\((\mu_2, \sigma_2)\)</span>,</p>
<p><span class="math display">\[
\begin{array}{rcl}
\mu_1, \mu_2 &amp; \sim &amp; \mathsf{normal}(0, 10)
\\[8pt]
\sigma_1, \sigma_2 &amp; \sim &amp; \mathsf{Halfnormal}(0, 10)
\end{