display">\[
x_K = 1 - \sum_{k=1}^{K-1} x_k.
\]</span></p>
<div id="unit-simplex-inverse-transform" class="section level3">
<h3>Unit Simplex Inverse Transform</h3>
<p>Stan’s unit simplex inverse transform may be understood using the
following stick-breaking metaphor.<a href="#fn15" class="footnote-ref" id="fnref15"><sup>15</sup></a></p>
<ol style="list-style-type: decimal">
<li>Take a stick of unit length (i.e., length 1).</li>
<li>Break a piece off and label it as <span class="math inline">\(x_1\)</span>,