become more and more concentrated below (not around) <span class="math inline">\(1/K\)</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 inlin