line">\(\sigma\)</span>. Gibbs will run quickly and provide
seemingly reasonable inferences for <span class="math inline">\(\lambda_1 + \lambda_2\)</span>. But it
will not explore the full range of the posterior; it will merely take
a slow random walk from the initial values. This random walk behavior
is typical of Gibbs sampling when posteriors are highly correlated and
the primary reason to prefer Hamiltonian Monte Carlo to Gibbs sampling
for models with parameters correlated in the posterior.</p>
</div>
