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Designing Bayesian Networks 2 [2* P]

Draw the graphical representation of a Bayesian network in which the following conditional independence relations hold:

$\displaystyle P(y_0, \ldots, y_T, s_0, \ldots, s_T) = P(s_0) \prod_{t=0}^T P(y_t \vert s_t) \prod_{t=1}^T P(s_t \vert s_{t-1}) $

Derive iterative update rules for inferring $ P(s_t \vert y_1, \ldots, y_t),  t=1, \ldots, T$ . For what kind of inference could you use such a model?

Pfeiffer Michael 2006-01-18