Update hiddenmarkovnormal.md

Author: RyoheiO

bayesml/hiddenmarkovnormal/hiddenmarkovnormal.md

@@ -43,9 +43,8 @@ $$
 \begin{align}
     p(\boldsymbol{\mu},\boldsymbol{\Lambda},\boldsymbol{\pi},\boldsymbol{A}) &= \left\{ \prod_{k=1}^K \mathcal{N}(\boldsymbol{\mu}_k|\boldsymbol{m}_0,(\kappa_0 \boldsymbol{\Lambda}_k)^{-1})\mathcal{W}(\boldsymbol{\Lambda}_k|\boldsymbol{W}_0, \nu_0) \right\} \mathrm{Dir}(\boldsymbol{\pi}|\boldsymbol{\eta}_0) \prod_{j=1}^{K}\mathrm{Dir}(\boldsymbol{a}_{j}|\boldsymbol{\zeta}_{0,j}), \\
     &= \Biggl[ \prod_{k=1}^K \left( \frac{\kappa_0}{2\pi} \right)^{D/2} |\boldsymbol{\Lambda}_k|^{1/2} \exp \left\{ -\frac{\kappa_0}{2}(\boldsymbol{\mu}_k -\boldsymbol{m}_0)^\top \boldsymbol{\Lambda}_k (\boldsymbol{\mu}_k - \boldsymbol{m}_0) \right\} \\
-    &\qquad \times B(\boldsymbol{W}_0, \nu_0) | \boldsymbol{\Lambda}_k |^{(\nu_0 - D - 1) / 2} \exp \left\{ -\frac{1}{2} \mathrm{Tr} \{ \boldsymbol{W}_0^{-1} \boldsymbol{\Lambda}_k \} \right\} \\
-    &\qquad \times C(\boldsymbol{\eta}_0)\pi_k^{\eta_{0,k}-1}\\
-    &\qquad \times \prod_{j=1}^KC(\boldsymbol{\zeta}_{0,j}) a_{jk}^{\zeta_{0,j,k}-1}\Biggr],\\
+    &\qquad \times B(\boldsymbol{W}_0, \nu_0) | \boldsymbol{\Lambda}_k |^{(\nu_0 - D - 1) / 2} \exp \left\{ -\frac{1}{2} \mathrm{Tr} \{ \boldsymbol{W}_0^{-1} \boldsymbol{\Lambda}_k \} \right\}\biggl] \\
+    &\qquad \times \Biggl[ \prod_{k=1}^KC(\boldsymbol{\eta}_0)\pi_k^{\eta_{0,k}-1}\biggl]\times \biggl[\prod_{j=1}^KC(\boldsymbol{\zeta}_{0,j})\prod_{k=1}^K a_{jk}^{\zeta_{0,j,k}-1}\Biggr],\\
 \end{align}
 $$