Update README.md

Author: flowel1

README.md

@@ -90,7 +90,7 @@ Gaussian prior:
 
 Lognormal prior:
 
-<a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\begin{matrix}&space;\phi(\underline{\delta})&space;\text{:&space;}&space;&&space;\frac{1}{2}&space;\beta_j^2(\log(\theta_j&space;&plus;&space;\delta_j)&space;-&space;\log\mu_j)^2&space;&plus;&space;\log(\theta_j&space;&plus;&space;\delta_j)&space;\sim&space;\\&space;\\&space;&&space;\frac{1}{2}&space;\beta_j^2(\log\theta_j&space;&plus;\frac{\delta_j}{\theta_j}&space;-&space;\log\mu_j)^2&space;&plus;\log\theta_j&space;&plus;\frac{\delta_j}{\theta_j}&space;\text{&space;}&space;\text{&space;}&space;\text{&space;}&space;\text{&space;}&space;\text{&space;}&space;\text{&space;}&space;\text{&space;}&space;\end{matrix}&space;\newline&space;\newline&space;\newline&space;\nabla_{\underline{\delta}}&space;\phi(\underline{\delta})_j&space;\text{:&space;}&space;-\frac{\beta_j^2}{\theta_j^2}&space;\cdot&space;\delta_j&space;&plus;&space;\{-&space;\frac{1}{\theta_j}&space;-\frac{\beta_j^2}{\theta_j}\log\frac{\theta_j}{\mu_j}&space;\}" target="_blank"><img src="https://latex.codecogs.com/svg.latex?\dpi{100}&space;\begin{matrix}&space;\phi(\underline{\delta})&space;\text{:&space;}&space;&&space;\frac{1}{2}&space;\beta_j^2(\log(\theta_j&space;&plus;&space;\delta_j)&space;-&space;\log\mu_j)^2&space;&plus;&space;\log(\theta_j&space;&plus;&space;\delta_j)&space;\sim&space;\\&space;\\&space;&&space;\frac{1}{2}&space;\beta_j^2(\log\theta_j&space;&plus;\frac{\delta_j}{\theta_j}&space;-&space;\log\mu_j)^2&space;&plus;\log\theta_j&space;&plus;\frac{\delta_j}{\theta_j}&space;\text{&space;}&space;\text{&space;}&space;\text{&space;}&space;\text{&space;}&space;\text{&space;}&space;\text{&space;}&space;\text{&space;}&space;\end{matrix}&space;\newline&space;\newline&space;\newline&space;\nabla_{\underline{\delta}}&space;\phi(\underline{\delta})_j&space;\text{:&space;}&space;-\frac{\beta_j^2}{\theta_j^2}&space;\cdot&space;\delta_j&space;&plus;&space;\{-&space;\frac{1}{\theta_j}&space;-\frac{\beta_j^2}{\theta_j}\log\frac{\theta_j}{\mu_j}&space;\}" title="\begin{matrix} \phi(\underline{\delta}) \text{: } & \frac{1}{2} \beta_j^2(\log(\theta_j + \delta_j) - \log\mu_j)^2 + \log(\theta_j + \delta_j) \sim \\ \\ & \frac{1}{2} \beta_j^2(\log\theta_j +\frac{\delta_j}{\theta_j} - \log\mu_j)^2 +\log\theta_j +\frac{\delta_j}{\theta_j} \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \end{matrix} \newline \newline \newline \nabla_{\underline{\delta}} \phi(\underline{\delta})_j \text{: } -\frac{\beta_j^2}{\theta_j^2} \cdot \delta_j + \{- \frac{1}{\theta_j} -\frac{\beta_j^2}{\theta_j}\log\frac{\theta_j}{\mu_j} \}" /></a>
+<a href="https://www.codecogs.com/eqnedit.php?latex=\dpi{100}&space;\begin{matrix}&space;\phi(\underline{\delta})&space;\text{:&space;}&space;&&space;\frac{1}{2}&space;\beta_j^2(\log(\theta_j&space;&plus;&space;\delta_j)&space;-&space;\log\mu_j)^2&space;&plus;&space;\log(\theta_j&space;&plus;&space;\delta_j)&space;\sim&space;\\&space;\\&space;&&space;\frac{1}{2}&space;\beta_j^2(\log\theta_j&space;&plus;\frac{\delta_j}{\theta_j}&space;-&space;\log\mu_j)^2&space;&plus;\log\theta_j&space;&plus;\frac{\delta_j}{\theta_j}&space;\text{&space;}&space;\text{&space;}&space;\text{&space;}&space;\text{&space;}&space;\text{&space;}&space;\text{&space;}&space;\text{&space;}&space;\end{matrix}&space;\newline&space;\newline&space;\newline&space;\nabla_{\underline{\delta}}&space;\phi(\underline{\delta})_j&space;\text{:&space;}&space;\text{&space;}&space;\text{&space;}&space;\frac{\beta_j^2}{\theta_j^2}&space;\cdot&space;\delta_j&space;&plus;&space;\{\frac{1}{\theta_j}&space;&plus;\frac{\beta_j^2}{\theta_j}\log\frac{\theta_j}{\mu_j}&space;\}" target="_blank"><img src="https://latex.codecogs.com/svg.latex?\dpi{100}&space;\begin{matrix}&space;\phi(\underline{\delta})&space;\text{:&space;}&space;&&space;\frac{1}{2}&space;\beta_j^2(\log(\theta_j&space;&plus;&space;\delta_j)&space;-&space;\log\mu_j)^2&space;&plus;&space;\log(\theta_j&space;&plus;&space;\delta_j)&space;\sim&space;\\&space;\\&space;&&space;\frac{1}{2}&space;\beta_j^2(\log\theta_j&space;&plus;\frac{\delta_j}{\theta_j}&space;-&space;\log\mu_j)^2&space;&plus;\log\theta_j&space;&plus;\frac{\delta_j}{\theta_j}&space;\text{&space;}&space;\text{&space;}&space;\text{&space;}&space;\text{&space;}&space;\text{&space;}&space;\text{&space;}&space;\text{&space;}&space;\end{matrix}&space;\newline&space;\newline&space;\newline&space;\nabla_{\underline{\delta}}&space;\phi(\underline{\delta})_j&space;\text{:&space;}&space;\text{&space;}&space;\text{&space;}&space;\frac{\beta_j^2}{\theta_j^2}&space;\cdot&space;\delta_j&space;&plus;&space;\{\frac{1}{\theta_j}&space;&plus;\frac{\beta_j^2}{\theta_j}\log\frac{\theta_j}{\mu_j}&space;\}" title="\begin{matrix} \phi(\underline{\delta}) \text{: } & \frac{1}{2} \beta_j^2(\log(\theta_j + \delta_j) - \log\mu_j)^2 + \log(\theta_j + \delta_j) \sim \\ \\ & \frac{1}{2} \beta_j^2(\log\theta_j +\frac{\delta_j}{\theta_j} - \log\mu_j)^2 +\log\theta_j +\frac{\delta_j}{\theta_j} \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \end{matrix} \newline \newline \newline \nabla_{\underline{\delta}} \phi(\underline{\delta})_j \text{: } \text{ } \text{ } \frac{\beta_j^2}{\theta_j^2} \cdot \delta_j + \{\frac{1}{\theta_j} +\frac{\beta_j^2}{\theta_j}\log\frac{\theta_j}{\mu_j} \}" /></a>
 
 (We have used the first-order expansion of log in the lognormal case).