| backward {HMM} | R Documentation |
Computes the backward probabilities
Description
The backward-function computes the backward probabilities.
The backward probability for state X and observation at time k is defined as the probability
of observing the sequence of observations e_k+1, ... ,e_n under the condition that the
state at time k is X. That is:
b[X,k] := Prob(E_k+1 = e_k+1, ... , E_n = e_n | X_k = X).
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.
Usage
backward(hmm, observation)
Arguments
hmm |
A Hidden Markov Model. |
observation |
A sequence of observations. |
Format
Dimension and Format of the Arguments.
- hmm
A valid Hidden Markov Model, for example instantiated by
initHMM.- observation
A vector of strings with the observations.
Value
Return Value:
backward |
A matrix containing the backward probabilities. The probabilities are given on a logarithmic scale (natural logarithm). The first dimension refers to the state and the second dimension to time. |
Author(s)
Lin Himmelmann <hmm@linhi.com>, Scientific Software Development
References
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 Also
See forward for computing the forward probabilities.
Examples
# 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 backward probablities
logBackwardProbabilities = backward(hmm,observations)
print(exp(logBackwardProbabilities))