e model will be applied to a clustering problem and
there might be two data items <span class="math inline">\(y_i\)</span> and <span class="math inline">\(y_j\)</span> for which there is a
question of whether they arose from the same mixture component. If we
take <span class="math inline">\(z_i\)</span> and <span class="math inline">\(z_j\)</span> to be the component responsibility discrete
variables, then the quantity of interest is <span class="math inline">\(z_i = z_j\)</span>, which can be
summarized as