# backward: Computes the backward probabilities In HMM: HMM - Hidden Markov Models

## 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

 1 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 <[email protected]>, 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 forward for computing the forward probabilities.

## Examples

 1 2 3 4 5 6 7 8 9 # 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))

HMM documentation built on May 29, 2017, 11:45 a.m.