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Hidden Markov model posterior state probabilities


PSTATES = hmmdecode(seq,TRANS,EMIS)
[PSTATES,logpseq] = hmmdecode(...)
[PSTATES,logpseq,FORWARD,BACKWARD,S] = hmmdecode(...)


PSTATES = hmmdecode(seq,TRANS,EMIS) calculates the posterior state probabilities, PSTATES, of the sequence seq, from a hidden Markov model. The posterior state probabilities are the conditional probabilities of being at state k at step i, given the observed sequence of symbols, sym. You specify the model by a transition probability matrix, TRANS, and an emissions probability matrix, EMIS. TRANS(i,j) is the probability of transition from state i to state j. EMIS(k,seq) is the probability that symbol seq is emitted from state k.

PSTATES is an array with the same length as seq and one row for each state in the model. The (i, j)th element of PSTATES gives the probability that the model is in state i at the jth step, given the sequence seq.


The function hmmdecode begins with the model in state 1 at step 0, prior to the first emission. hmmdecode computes the probabilities in PSTATES based on the fact that the model begins in state 1.

[PSTATES,logpseq] = hmmdecode(...) returns logpseq, the logarithm of the probability of sequence seq, given transition matrix TRANS and emission matrix EMIS.

[PSTATES,logpseq,FORWARD,BACKWARD,S] = hmmdecode(...) returns the forward and backward probabilities of the sequence scaled by S.

hmmdecode(...,'Symbols',SYMBOLS) specifies the symbols that are emitted. SYMBOLS can be a numeric array, a string array, or a cell array of the names of the symbols. The default symbols are integers 1 through N, where N is the number of possible emissions.


trans = [0.95,0.05;
emis = [1/6 1/6 1/6 1/6 1/6 1/6;
   1/10 1/10 1/10 1/10 1/10 1/2];
[seq,states] = hmmgenerate(100,trans,emis);
pStates = hmmdecode(seq,trans,emis);
[seq,states] = hmmgenerate(100,trans,emis,...
pStates = hmmdecode(seq,trans,emis,...


[1] Durbin, R., S. Eddy, A. Krogh, and G. Mitchison. Biological Sequence Analysis. Cambridge, UK: Cambridge University Press, 1998.

Version History

Introduced before R2006a