>Consider what happens with initial values <span class="math inline">\(\lambda_1^{(0)}, \lambda_2^{(0)}\)</span>.
Gibbs sampling proceeds in iteration <span class="math inline">\(m\)</span> by drawing</p>
<p><span class="math display">\[
\begin{array}{rcl}
\lambda_1^{(m)}
&amp; \sim &amp; p(\lambda_1 \, | \, \lambda_2^{(m-1)}, \, \sigma^{(m-1)}, \, y)
\\[6pt]
\lambda_2^{(m)}
&amp; \sim &amp; p(\lambda_2 \, | \, \lambda_1^{(m)}, \, \sigma^{(m-1)}, \, y)
\\[6pt]
\sigma^{(m)}
&amp; \sim &amp; p(\sigma \, | \, 