amples. They demonstrate the need for careful methods to decide whether a finite sample originated from a single population. (Granted, this single population contains <span class="math inline">\(2^P\)</span> clusters, but for large values of <span class="math inline">\(P\)</span> one needs exponentially larger values of <span class="math inline">\(N\)</span> to capture these clusters. This is why we often do not consider clustering a sample into <span class="math inline">\(2^P\)</span> roughly evenly-sized 