Update README.md

Author: flowel1

README.md

@@ -78,7 +78,7 @@ Reasoning in Bayesian terms, this time we estimate <ins>&theta;</ins> via **maxi
 
 Keeping the same notations as before, the objective function to minimize is now
 
-<a href="https://www.codecogs.com/eqnedit.php?latex=\text{Obj}(\underline{\theta})&space;=&space;-\log&space;p(\underline{\theta}&space;|&space;X,&space;\underline{y})&space;=&space;\newline&space;\newline&space;=&space;\text{const}&space;&plus;\frac{N}{2}&space;\log(\sigma^2)&space;&plus;\frac{1}{2\sigma^2}&space;\left&space;\|&space;W&space;\cdot&space;(\underline{y}&space;-&space;f(X,&space;\underline{\theta}))&space;\right&space;\|^2&space;&plus;&space;\newline&space;\newline&space;&plus;\frac{1}{2}&space;\cdot&space;\sum_{\{j&space;|&space;p(\theta_j)&space;\text{&space;gaussian}\}}&space;\beta_j&space;(\theta_j&space;-&space;\mu_j)^2&space;\newline&space;\newline&space;&plus;\frac{1}{2}&space;\cdot&space;\sum_{\{j&space;|&space;p(\theta_j)&space;\text{&space;lognormal}\}}&space;\{&space;\log\theta_j&space;&plus;&space;\beta_j&space;(\log\theta_j&space;-&space;\log\mu_j)^2\}" target="_blank"><img src="https://latex.codecogs.com/svg.latex?\text{Obj}(\underline{\theta})&space;=&space;-\log&space;p(\underline{\theta}&space;|&space;X,&space;\underline{y})&space;=&space;\newline&space;\newline&space;=&space;\text{const}&space;&plus;\frac{N}{2}&space;\log(\sigma^2)&space;&plus;\frac{1}{2\sigma^2}&space;\left&space;\|&space;W&space;\cdot&space;(\underline{y}&space;-&space;f(X,&space;\underline{\theta}))&space;\right&space;\|^2&space;&plus;&space;\newline&space;\newline&space;&plus;\frac{1}{2}&space;\cdot&space;\sum_{\{j&space;|&space;p(\theta_j)&space;\text{&space;gaussian}\}}&space;\beta_j&space;(\theta_j&space;-&space;\mu_j)^2&space;\newline&space;\newline&space;&plus;\frac{1}{2}&space;\cdot&space;\sum_{\{j&space;|&space;p(\theta_j)&space;\text{&space;lognormal}\}}&space;\{&space;\log\theta_j&space;&plus;&space;\beta_j&space;(\log\theta_j&space;-&space;\log\mu_j)^2\}" title="\text{Obj}(\underline{\theta}) = -\log p(\underline{\theta} | X, \underline{y}) = \newline \newline = \text{const} +\frac{N}{2} \log(\sigma^2) +\frac{1}{2\sigma^2} \left \| W \cdot (\underline{y} - f(X, \underline{\theta})) \right \|^2 + \newline \newline +\frac{1}{2} \cdot \sum_{\{j | p(\theta_j) \text{ gaussian}\}} \beta_j (\theta_j - \mu_j)^2 \newline \newline +\frac{1}{2} \cdot \sum_{\{j | p(\theta_j) \text{ lognormal}\}} \{ \log\theta_j + \beta_j (\log\theta_j - \log\mu_j)^2\}" /></a>
+<a href="https://www.codecogs.com/eqnedit.php?latex=\text{Obj}(\underline{\theta})&space;=&space;-\log&space;p(\underline{\theta}&space;|&space;X,&space;\underline{y})&space;=&space;\newline&space;\newline&space;=&space;\text{const}&space;&plus;\frac{N}{2}&space;\log(\sigma^2)&space;&plus;\frac{1}{2\sigma^2}&space;\left&space;\|&space;W&space;\cdot&space;(\underline{y}&space;-&space;f(X,&space;\underline{\theta}))&space;\right&space;\|^2&space;&plus;&space;\newline&space;\newline&space;&plus;\frac{1}{2}&space;\cdot&space;\sum_{\{j&space;|&space;p(\theta_j)&space;\text{&space;gaussian}\}}&space;\beta_j&space;(\theta_j&space;-&space;\mu_j)^2&space;\newline&space;\newline&space;&plus;\sum_{\{j&space;|&space;p(\theta_j)&space;\text{&space;lognormal}\}}&space;\{&space;\log\theta_j&space;&plus;\frac{1}{2}&space;\beta_j&space;(\log\theta_j&space;-&space;\log\mu_j)^2\}" target="_blank"><img src="https://latex.codecogs.com/svg.latex?\text{Obj}(\underline{\theta})&space;=&space;-\log&space;p(\underline{\theta}&space;|&space;X,&space;\underline{y})&space;=&space;\newline&space;\newline&space;=&space;\text{const}&space;&plus;\frac{N}{2}&space;\log(\sigma^2)&space;&plus;\frac{1}{2\sigma^2}&space;\left&space;\|&space;W&space;\cdot&space;(\underline{y}&space;-&space;f(X,&space;\underline{\theta}))&space;\right&space;\|^2&space;&plus;&space;\newline&space;\newline&space;&plus;\frac{1}{2}&space;\cdot&space;\sum_{\{j&space;|&space;p(\theta_j)&space;\text{&space;gaussian}\}}&space;\beta_j&space;(\theta_j&space;-&space;\mu_j)^2&space;\newline&space;\newline&space;&plus;\sum_{\{j&space;|&space;p(\theta_j)&space;\text{&space;lognormal}\}}&space;\{&space;\log\theta_j&space;&plus;\frac{1}{2}&space;\beta_j&space;(\log\theta_j&space;-&space;\log\mu_j)^2\}" title="\text{Obj}(\underline{\theta}) = -\log p(\underline{\theta} | X, \underline{y}) = \newline \newline = \text{const} +\frac{N}{2} \log(\sigma^2) +\frac{1}{2\sigma^2} \left \| W \cdot (\underline{y} - f(X, \underline{\theta})) \right \|^2 + \newline \newline +\frac{1}{2} \cdot \sum_{\{j | p(\theta_j) \text{ gaussian}\}} \beta_j (\theta_j - \mu_j)^2 \newline \newline +\sum_{\{j | p(\theta_j) \text{ lognormal}\}} \{ \log\theta_j +\frac{1}{2} \beta_j (\log\theta_j - \log\mu_j)^2\}" /></a>
 
 (the term const incorporates terms that are independent of both <ins>&theta;</ins> and &sigma;). This corresponds to minimizing a weighted sum of squared residuals plus a series of regularization terms.