Then, the likelihood of the observations given the parameters can be computed as follows Note that the following equation holds: where the right-hand side is actually the expansion .
the likelihood can be simplified as Switching to the notations w j and o k , we have where δ w i,j = 1 ifw i,j ∈ w i and δ w i,j = 0 otherwise, and δ o i,k = 1 ifõ i,k ∈ o i and δ o i,k = 0 otherwise.