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Initial state probabilities should be pi_0 throughout for consistency |
pi_0 for initial state probabilities |
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Line 137:
:<math>
\mathbf{\gamma_t}(i) =
\mathbf{P}(X_t=x_i | o_1, o_2, \dots, o_T, \mathbf{\pi}_0) =
\frac{ \mathbf{P}(o_1, o_2, \dots, o_T, X_t=x_i | \mathbf{\pi}_0 ) }{ \mathbf{P}(o_1, o_2, \dots, o_T | \mathbf{\pi}_0 ) } =
\frac{ \mathbf{f_{0:t}}(i) \cdot \mathbf{b_{t:T}}(i) }{ \prod_{s=1}^T c_s } =
\mathbf{\hat{f}_{0:t}}(i) \cdot \mathbf{\hat{b}_{t:T}}(i)
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