{\beta})
</script>

<p>Again, after pulling out $\sigma^2$ and ignoring the constant, it gets transformed into</p>

<script type="math/tex; mode=display">
-\frac12(N-D)\log(2\pi) +\frac12\log\left|X^TX\right| - \left(\frac{N}{2}\log(\sigma^2) + \frac12\log|\gamma K+ I|\right)
-\left(-\frac{D}{2}\log(\sigma^2)+\frac12\log\left|X^T(\gamma K+ I)^{-1}X\right|\right) - \frac{N-D}{2}
</script>

<p>which simplifies to</p>

<script type="math/tex; mode=display">
-\frac12(N-D)\log(2\pi\sigma^2) - \frac12\log|\gamma 