Nonstationary hidden Markov model estimation

John uebersaxjohn2000 at
Tue Mar 16 13:00:35 EST 2004

Does anyone know if the "Forward Algorithm" to estimate:

   Pr(o1, o2, ..., oT | theta),


   o1, o2, ..., OT = observed states at T timepoints or sequence
   theta           = a vector of parameters that define a hidden 
                     Markov model

is correct if transition probability parameters are nonstationary?  

That is, does the Forward Algorithm give the same value as the full 
expansion of the likelihood function if the probabilities of moving
from state i to state j differ from one period/sequence position to 

I'm unable to find any reference to this despite a fairly thorough web
search, but it seems like an obvious question.

John Uebersax

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