k,k} =
\left\{
\begin{array}{ll}
1 &amp; \mbox{if } k = 1, \mbox{ and}
\\
\exp(y_k) &amp; \mbox{if } 1 &lt; k \leq K.
\end{array}
\right.
\]</span></p>
<p>Because <span class="math inline">\(J\)</span> is triangular, the absolute Jacobian determinant is</p>
<p><span class="math display">\[
\left| \, \det \, J \, \right|
\ = \
\left| \, \prod_{k=1}^K J_{k,k} \, \right|
\ = \
\prod_{k=2}^K \exp(y_k).
\]</span></p>
<p>Putting this all together, if <span class="math inline">\(p_X\)</span> is the density of <spa