p>
</div>
<div id="ordered-inverse-transform" class="section level3">
<h3 class="unnumbered" number="">Ordered Inverse Transform</h3>
<p>The inverse transform for an unconstrained <span class="math inline">\(y \in \mathbb{R}^K\)</span> to an
ordered sequence <span class="math inline">\(x \in \mathbb{R}^K\)</span> is defined by the recursion</p>
<p><span class="math display">\[
x_k
=
\left\{
\begin{array}{ll}
y_1 &amp; \mbox{if } k = 1, \mbox{ and}
\\
x_{k-1} + \exp(y_k) &amp; \mbox{if } 1 &lt; k \leq K.
\en