[\begin{equation*}
(\mathbf{x}_1,\ldots,\mathbf{x}_N) \overset{D}{=}(\mathbf{x}_{\pi(1)},\ldots,\mathbf{x}_{\pi(N)})
\end{equation*}\]</span> for each permutation <span class="math inline">\(\pi\)</span> of <span class="math inline">\(\{1,\ldots,N\}\)</span>. This definition is relevant to sampling from a population: a finite sample drawn via random sampling from a large population is exchangeable.</p>
<p>So how can exchangeability help us avoid parametric modelling while detecting the existence of subpopul