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Discrete HMM

The hidden states are $s_t\in\{1,2,\dots,S\}$ and the observed variables are $x_t\in\{1,2,\dots,N\}$ . The transition probabilities are that of a Markov chain, and the observation probabilities are

$\displaystyle p(s_t=i\vert s_{t-1}=j)$	$\displaystyle =$	$\displaystyle A_{ij}$	(27)
$\displaystyle p(x_t=i\vert s_t=j)$	$\displaystyle =$	$\displaystyle B_{ij}$	(28)

Markus Mayer 2009-06-22