## The standard HMM

Following the notation of Rabiner [57], there are observation times. At each time , there is a discrete state variable which takes one of values . According to the Markovian assumption, the probability distribution of depends only on the value of . This is described compactly as a state transition probability matrix whose elements represent the probability that equals given that equals . The initial state probabilities are denoted , the probability that equals .

It is a hidden Markov model because the states are hidden from view; we cannot observe them. But, we can observe the random data which is generated according to a PDF dependent on the state at time . We denote the PDF of under state as .

The complete set of model parameters that define the HMM are

The Baum-Welch algorithm calculates new estimates given an observation sequence and a previous estimate of . The algorithm is composed of two parts: the forward/backward procedure, and the reestimation of parameters.

Subsections
Baggenstoss 2017-05-19