The re-estimation formulae for the embedded model case have to be modified to take account of the fact that the entry states can be occupied at any time as a result of transitions out of the previous model. The basic formulae for the re-estimation of the transition probabilities is
The transitions from the non-emitting entry states into the HMM are re-estimated by
and the transitions out of the HMM into the non-emitting exit states are re-estimated by
Finally, the direct transitions from non-emitting entry to non-emitting exit states are re-estimated by
The re-estimation formulae for the output distributions are the
same as for the single model case except
for the obvious additional subscript for q. However, the
probability calculations must now allow for transitions from the
entry states by changing 
in equation 8.1 to
