This commit is contained in:
Morten Hjorth-Jensen
2022-09-15 08:08:44 +02:00
parent a077df41d6
commit 24ce30160a
7 changed files with 158 additions and 158 deletions
+2 -2
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@@ -113,13 +113,13 @@ We could now define a new cost function to minimize, namely the negative logarit
!bt
\[
C(\bm{\beta}=-\log{\prod_{i=0}^{n-1}p(y_i,\bm{X}\vert\bm{\beta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\bm{X}\vert\bm{\beta})},
C(\bm{\beta})=-\log{\prod_{i=0}^{n-1}p(y_i,\bm{X}\vert\bm{\beta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\bm{X}\vert\bm{\beta})},
\]
!et
which becomes
!bt
\[
C(\bm{\beta}=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\bm{y}-\bm{X}\bm{\beta})\vert\vert_2^2}{2\sigma^2}.
C(\bm{\beta})=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\bm{y}-\bm{X}\bm{\beta})\vert\vert_2^2}{2\sigma^2}.
\]
!et