Merge pull request #73 from StatProofBook/master

update to master

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) \; ,

I/PbA.md

@@ -4,7 +4,7 @@ title: "Proof by Author"
 ---
 
 
-### JoramSoch (283 proofs)
+### JoramSoch (286 proofs)
 
 - [(Non-)Multiplicativity of the expected value](/P/mean-mult)
 - [Accuracy and complexity for the univariate Gaussian](/P/ug-anc)
@@ -89,7 +89,10 @@ title: "Proof by Author"
 - [Invariance of the variance under addition of a constant](/P/var-inv)
 - [Inverse transformation method using cumulative distribution function](/P/cdf-itm)
 - [Joint likelihood is the product of likelihood function and prior density](/P/jl-lfnprior)
+- [Kullback-Leibler divergence for the Dirichlet distribution](/P/dir-kl)
+- [Kullback-Leibler divergence for the Wishart distribution](/P/wish-kl)
 - [Kullback-Leibler divergence for the gamma distribution](/P/gam-kl)
+- [Kullback-Leibler divergence for the matrix-normal distribution](/P/matn-kl)
 - [Kullback-Leibler divergence for the multivariate normal distribution](/P/mvn-kl)
 - [Kullback-Leibler divergence for the normal distribution](/P/norm-kl)
 - [Kullback-Leibler divergence for the normal-gamma distribution](/P/ng-kl)

I/PbN.md

@@ -299,3 +299,6 @@ title: "Proof by Number"
 | P291 | mean-tot | [Law of total expectation](/P/mean-tot) | JoramSoch | 2021-11-26 |
 | P292 | var-tot | [Law of total variance](/P/var-tot) | JoramSoch | 2021-11-26 |
 | P293 | cov-tot | [Law of total covariance](/P/cov-tot) | JoramSoch | 2021-11-26 |
+| P294 | dir-kl | [Kullback-Leibler divergence for the Dirichlet distribution](/P/dir-kl) | JoramSoch | 2021-12-02 |
+| P295 | wish-kl | [Kullback-Leibler divergence for the Wishart distribution](/P/wish-kl) | JoramSoch | 2021-12-02 |
+| P296 | matn-kl | [Kullback-Leibler divergence for the matrix-normal distribution](/P/matn-kl) | JoramSoch | 2021-12-02 |

I/PbT.md

@@ -117,10 +117,13 @@ title: "Proof by Topic"
 
 ### K
 
+- [Kullback-Leibler divergence for the Dirichlet distribution](/P/dir-kl)
 - [Kullback-Leibler divergence for the gamma distribution](/P/gam-kl)
+- [Kullback-Leibler divergence for the matrix-normal distribution](/P/matn-kl)
 - [Kullback-Leibler divergence for the multivariate normal distribution](/P/mvn-kl)
 - [Kullback-Leibler divergence for the normal distribution](/P/norm-kl)
 - [Kullback-Leibler divergence for the normal-gamma distribution](/P/ng-kl)
+- [Kullback-Leibler divergence for the Wishart distribution](/P/wish-kl)
 
 ### L
 

I/PwS.md

@@ -27,6 +27,7 @@ title: "Proofs without Source"
 - [Exponential distribution is a special case of gamma distribution](/P/exp-gam)
 - [First raw moment is mean](/P/momraw-1st)
 - [Joint likelihood is the product of likelihood function and prior density](/P/jl-lfnprior)
+- [Kullback-Leibler divergence for the matrix-normal distribution](/P/matn-kl)
 - [Kullback-Leibler divergence for the normal distribution](/P/norm-kl)
 - [Linear combination of independent normal random variables](/P/norm-lincomb)
 - [Linear transformation theorem for the matrix-normal distribution](/P/matn-ltt)

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