Hidden Semi-Markov Models

${\hat{b}}_j(v)=\underset{k=1}{\sum ^n}\underset{t=1}{\sum ^{T_k}}\left[\frac{{\gamma }_t^{(k)}(j)}{P\left[{\mathbf{o}}^{(k)}\right|\lambda ]}\cdot I(o_t^{(k)}=v)\right],$

and

${\hat{\pi }}_j=\underset{k=1}{\sum ^n}\frac{{\gamma }_0^{(k)}(j)}{P\left[{\mathbf{o}}^{(k)}\right|\lambda ]},$

subject to ${\displaystyle \sum }_{j\ne i}{\hat{a}}_{ij}=1,{\displaystyle \sum }_d{\hat{p}}_j(d)=1$, and ${\displaystyle \sum }_{v_k}{b}_j(v_k)=1$, where ${\gamma }_t^{(k)}(j)$ are corresponding to the $k$th observation sequence.

Algorithm 3.2

Re-estimation Algorithm for Multiple ...