</span>. When one
component of the simplex is large, the others must all be relatively
small to compensate. For example, in a uniform distribution on
<span class="math inline">\(10\)</span>-simplexes, the probability that a component is greater than the
mean of <span class="math inline">\(1/10\)</span> is only 39%. Most of the posterior marginal
probability mass for each component is in the interval <span class="math inline">\((0, 0.1)\)</span>.</p>
<p>When the <span class="math inline">\(\alpha\)</span> va