HMM (version 1.0.1)

backward: 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.

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.

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.

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

# NOT RUN {
# 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))
# }