[
\begin{array}{ccc}
1 &amp; 0 &amp; 0
\\
z_{2,1} &amp; \sqrt{1 - x_{2,1}^2} &amp; 0
\\
z_{3,1} &amp; z_{3,2} \sqrt{1 - x_{3,1}^2}
        &amp; \sqrt{1 - (x_{3,1}^2 + x_{3,2}^2)}
\end{array}
\right],
\]</span></p>
<p>where the <span class="math inline">\(z_{i,j} \in (-1,1)\)</span> are the <span class="math inline">\(\tanh\)</span>-transformed <span class="math inline">\(y\)</span>.</p>
<p>The approach is a signed stick-breaking process on the quadratic
(Euclidean length) scale. Starting from length 1 at <