corrected some pages

Several small mistakes/errors were corrected in several proofs/definitions.

Author: JoramSoch

D/dir.md

@@ -27,7 +27,7 @@ username: "JoramSoch"
 ---
 
 
-**Definition:** Let $X$ be a [random vector](/D/rvec). Then, $X$ is said to follow a Dirichlet distribution with concentration parameters $\alpha = \left[ \alpha_1, \ldots, \alpha_k \right]$
+**Definition:** Let $X$ be a $k \times 1$ [random vector](/D/rvec). Then, $X$ is said to follow a Dirichlet distribution with concentration parameters $\alpha = \left[ \alpha_1, \ldots, \alpha_k \right]$
 
 $$ \label{eq:Dir}
 X \sim \mathrm{Dir}(\alpha) \; ,

P/gam-kl.md

@@ -31,7 +31,7 @@ username: "JoramSoch"
 $$ \label{eq:gams}
 \begin{split}
 P: \; X &\sim \mathrm{Gam}(a_1, b_1) \\
-Q: \; X &\sim \mathrm{Gam}(a_2, b_2) \; . \\
+Q: \; X &\sim \mathrm{Gam}(a_2, b_2) \; .
 \end{split}
 $$
 

P/matn-mvn.md

@@ -36,7 +36,7 @@ $$
 if and only if $\mathrm{vec}(X)$ is [multivariate normally distributed](/D/mvn)
 
 $$ \label{eq:mvn}
-\mathrm{vec}(X) \sim \mathcal{MN}(\mathrm{vec}(M), V \otimes U)
+\mathrm{vec}(X) \sim \mathcal{N}(\mathrm{vec}(M), V \otimes U)
 $$
 
 where $\mathrm{vec}(X)$ is the vectorization operator and $\otimes$ is the Kronecker product.

P/mvn-kl.md

@@ -31,7 +31,7 @@ username: "JoramSoch"
 $$ \label{eq:mvns}
 \begin{split}
 P: \; x &\sim \mathcal{N}(\mu_1, \Sigma_1) \\
-Q: \; x &\sim \mathcal{N}(\mu_2, \Sigma_2) \; . \\
+Q: \; x &\sim \mathcal{N}(\mu_2, \Sigma_2) \; .
 \end{split}
 $$
 

P/ng-kl.md

@@ -32,7 +32,7 @@ username: "JoramSoch"
 $$ \label{eq:NGs}
 \begin{split}
 P: \; (x,y) &\sim \mathrm{NG}(\mu_1, \Lambda_1^{-1}, a_1, b_1) \\
-Q: \; (x,y) &\sim \mathrm{NG}(\mu_2, \Lambda_2^{-1}, a_2, b_2) \; . \\
+Q: \; (x,y) &\sim \mathrm{NG}(\mu_2, \Lambda_2^{-1}, a_2, b_2) \; .
 \end{split}
 $$
 

P/norm-kl.md

@@ -26,7 +26,7 @@ username: "JoramSoch"
 $$ \label{eq:norms}
 \begin{split}
 P: \; X &\sim \mathcal{N}(\mu_1, \sigma_1^2) \\
-Q: \; X &\sim \mathcal{N}(\mu_2, \sigma_2^2) \; . \\
+Q: \; X &\sim \mathcal{N}(\mu_2, \sigma_2^2) \; .
 \end{split}
 $$
 

P/wish-kl.md

@@ -56,7 +56,7 @@ $$
 
 and $\psi_p(x)$ is the multivariate digamma function
 
-$$ \label{eq:mult-gam-fct}
+$$ \label{eq:mult-psi-fct}
 \psi_p(x) = \frac{\mathrm{d}\ln \Gamma_p(x)}{\mathrm{d}x} = \sum_{j=1}^k \psi\left(x - \frac{j-1}{2}\right) \; .
 $$