posterior | R Documentation |
This function computes the posterior probabilities of being in state X at time k for a given sequence of observations and a given Hidden Markov Model.
posterior(hmm, observation)
hmm |
A Hidden Markov Model. |
observation |
A sequence of observations. |
Dimension and Format of the Arguments.
A valid Hidden Markov Model, for example instantiated by initHMM
.
A vector of observations.
The posterior probability of being in a state X at time k can be computed from the
forward
and backward
probabilities:
Ws(X_k = X | E_1 = e_1, ... , E_n = e_n) = f[X,k] * b[X,k] / Prob(E_1 = e_1, ... , E_n = e_n)
Where E_1...E_n = e_1...e_n
is the sequence of observed emissions and
X_k
is a random variable that represents the state at time k
.
Return Values:
posterior |
A matrix containing the posterior probabilities. The first dimension refers to the state and the second dimension to time. |
Lin Himmelmann <hmm@linhi.com>, Scientific Software Development
Lawrence R. Rabiner: A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition. Proceedings of the IEEE 77(2) p.257-286, 1989.
See forward
for computing the forward probabilities and backward
for computing the backward probabilities.
# Initialise HMM hmm = initHMM(c("A","B"), c("L","R"), transProbs=matrix(c(.8,.2,.2,.8),2), emissionProbs=matrix(c(.6,.4,.4,.6),2)) print(hmm) # Sequence of observations observations = c("L","L","R","R") # Calculate posterior probablities of the states posterior = posterior(hmm,observations) print(posterior)
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