update

Author: mhjensen

doc/pub/week38/html/._week38-bs010.html

@@ -256,12 +256,12 @@ <h2 id="a-new-cost-function" class="anchor">A new Cost Function </h2>
 <p>We could now define a new cost function to minimize, namely the negative logarithm of the above PDF</p>
 
 $$
-C(\boldsymbol{\theta}=-\log{\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\theta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\boldsymbol{X}\vert\boldsymbol{\theta})},
+C(\boldsymbol{\theta})=-\log{\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\theta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\boldsymbol{X}\vert\boldsymbol{\theta})},
 $$
 
 <p>which becomes</p>
 $$
-C(\boldsymbol{\theta}=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\theta})\vert\vert_2^2}{2\sigma^2}.
+C(\boldsymbol{\theta})=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\theta})\vert\vert_2^2}{2\sigma^2}.
 $$
 
 <p>Taking the derivative of the <em>new</em> cost function with respect to the parameters \( \theta \) we recognize our familiar OLS equation, namely</p>

doc/pub/week38/html/week38-reveal.html

@@ -526,14 +526,14 @@ <h2 id="a-new-cost-function">A new Cost Function </h2>
 
 <p>&nbsp;<br>
 $$
-C(\boldsymbol{\theta}=-\log{\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\theta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\boldsymbol{X}\vert\boldsymbol{\theta})},
+C(\boldsymbol{\theta})=-\log{\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\theta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\boldsymbol{X}\vert\boldsymbol{\theta})},
 $$
 <p>&nbsp;<br>
 
 <p>which becomes</p>
 <p>&nbsp;<br>
 $$
-C(\boldsymbol{\theta}=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\theta})\vert\vert_2^2}{2\sigma^2}.
+C(\boldsymbol{\theta})=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\theta})\vert\vert_2^2}{2\sigma^2}.
 $$
 <p>&nbsp;<br>
 

doc/pub/week38/html/week38-solarized.html

@@ -527,12 +527,12 @@ <h2 id="a-new-cost-function">A new Cost Function </h2>
 <p>We could now define a new cost function to minimize, namely the negative logarithm of the above PDF</p>
 
 $$
-C(\boldsymbol{\theta}=-\log{\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\theta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\boldsymbol{X}\vert\boldsymbol{\theta})},
+C(\boldsymbol{\theta})=-\log{\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\theta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\boldsymbol{X}\vert\boldsymbol{\theta})},
 $$
 
 <p>which becomes</p>
 $$
-C(\boldsymbol{\theta}=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\theta})\vert\vert_2^2}{2\sigma^2}.
+C(\boldsymbol{\theta})=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\theta})\vert\vert_2^2}{2\sigma^2}.
 $$
 
 <p>Taking the derivative of the <em>new</em> cost function with respect to the parameters \( \theta \) we recognize our familiar OLS equation, namely</p>

doc/pub/week38/html/week38.html

@@ -604,12 +604,12 @@ <h2 id="a-new-cost-function">A new Cost Function </h2>
 <p>We could now define a new cost function to minimize, namely the negative logarithm of the above PDF</p>
 
 $$
-C(\boldsymbol{\theta}=-\log{\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\theta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\boldsymbol{X}\vert\boldsymbol{\theta})},
+C(\boldsymbol{\theta})=-\log{\prod_{i=0}^{n-1}p(y_i,\boldsymbol{X}\vert\boldsymbol{\theta})}=-\sum_{i=0}^{n-1}\log{p(y_i,\boldsymbol{X}\vert\boldsymbol{\theta})},
 $$
 
 <p>which becomes</p>
 $$
-C(\boldsymbol{\theta}=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\theta})\vert\vert_2^2}{2\sigma^2}.
+C(\boldsymbol{\theta})=\frac{n}{2}\log{2\pi\sigma^2}+\frac{\vert\vert (\boldsymbol{y}-\boldsymbol{X}\boldsymbol{\theta})\vert\vert_2^2}{2\sigma^2}.
 $$
 
 <p>Taking the derivative of the <em>new</em> cost function with respect to the parameters \( \theta \) we recognize our familiar OLS equation, namely</p>