-momentum-variable" class="section level3">
<h3>Auxiliary Momentum Variable</h3>
<p>HMC introduces auxiliary momentum variables <span class="math inline">\(\rho\)</span> and draws from a
joint density</p>
<p><span class="math display">\[
p(\rho, \theta) = p(\rho | \theta) p(\theta).
\]</span></p>
<p>In most applications of HMC, including Stan, the auxiliary density is
a multivariate normal that does not depend on the parameters <span class="math inline">\(\theta\)</span>,</p>
<p><span class="math display">\