Backward algorithm
= Backward algorithm
{title2=$\beta_t(i)$}
The <backward algorithm> computes suffix likelihoods in a <Hidden Markov model>. With $\beta_t(i)=P(o_{t+1},\ldots,o_T\mid Z_t=i)$, its recurrence is $\beta_t(i)=\sum_j a_{ij}b_j(o_{t+1})\beta_{t+1}(j)$. Together with the <forward algorithm>, it gives posterior state probabilities proportional to $\alpha_t(i)\beta_t(i)$. The terminal condition must include any explicit End-state transition.