\(L\)</span>
is a constant is to shift a lower-bounded parameter.</p>
<pre><code>data {
  int N;
  vector[N] L;  // lower bounds
  ...
parameters {
  vector&lt;lower=0&gt;[N] alpha_raw;
  ...
transformed parameters {
  vector[N] alpha = L + alpha_raw;
  ...</code></pre>
<p>The Jacobian for adding a constant is one, so its log drops out of the
log density.</p>
<p>Even if the lower bound is a parameter rather than data, there is no
Jacobian required, because the transform from <span class="math inline">\((L, 