Forward–backward algorithm: Difference between revisions

Revision as of 18:35, 27 November 2013

Revision as of 18:43, 27 November 2013

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We transform the probability distributions related to a given [[hidden Markov model]] into matrix notation as follows.

The transition probabilities <math>\mathbf{P}(X_t\mid X_{t-1})</math> of a given random variable <math>X_t</math> representing all possible states in the hidden Markov model will be represented by the matrix <math>\mathbf{T}</math> where the row index, i, will represent the targetstart state and the column index, j, represents the starttarget state. The example below represents a system where the probability of staying in the same state after each step is 70% and the probability of transitioning to the other state is 30%. The transition matrix is then:

:<math>\mathbf{T} = \begin{pmatrix}