The probability of node t being assigned state k is given by: where s(t) denotes the set of siblings of t, f −xt k (x t ) denotes the posterior probability of observation x t given all other observations assigned to state k, and z −t denotes all state assignments except z t .
the probability is proportional to the product of three terms: the probability of the states of t and its siblings given its parent z p(t) , the probability of the states of the children c(t) given z t , and the posterior probability of observation x t given z t .