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${\stackrel{ˆ}{b}}_{j}\left(v\right)=\underset{k=1}{\sum ^{n}}\underset{t=1}{\sum ^{{T}_{k}}}\left[\frac{{\gamma }_{t}^{\left(k\right)}\left(j\right)}{P\left[{\mathbf{o}}^{\left(k\right)}|\lambda \right]}\cdot I\left({o}_{t}^{\left(k\right)}=v\right)\right],$

and

${\stackrel{ˆ}{\pi }}_{j}=\underset{k=1}{\sum ^{n}}\frac{{\gamma }_{0}^{\left(k\right)}\left(j\right)}{P\left[{\mathbf{o}}^{\left(k\right)}|\lambda \right]},$

subject to $\sum _{j\ne i}{\stackrel{ˆ}{a}}_{ij}=1,\sum _{d}{\stackrel{ˆ}{p}}_{j}\left(d\right)=1$, and $\sum _{{v}_{k}}{b}_{j}\left({v}_{k}\right)=1$, where ${\gamma }_{t}^{\left(k\right)}\left(j\right)$ are corresponding to the $k$th observation sequence.

Algorithm 3.2

Re-estimation Algorithm for Multiple ...

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