Hidden Markov Models

We use the forward algorithm to calculate the probability of an observation sequence given a particular HMM, and hence choose the most probable HMM.

This type of problem occurs in speech recognition where a large number of Markov models will be used, each one modelling a particular word. An observation sequence is formed from a spoken word, and this word is recognised by identifying the most probable HMM for the observations.

2. Decoding

Another related problem, and the one usually of most interest, is to find the hidden states that generated the observed output. In many cases we are interested in the hidden states of the model since they represent something of value that is not directly observable.