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Multitype branching processes (MTBP) model branching structures, where thenodes of the resulting tree are objects of different types. One field ofapplication of such models in biology is in studies of cell proliferation. Asampling scheme that appears frequently is observing the cell count in severalindependent colonies at discrete time points (sometimes only one). Thus, theprocess is not observable in the sense of the whole tree, but only as the"generation" at given moment in time, which consist of the number of cells ofevery type. This requires an EM-type algorithm to obtain a maximum likelihood(ML) estimation of the parameters of the branching process. A computationalapproach for obtaining such estimation of the offspring distribution ispresented in the class of Markov branching processes with terminal types.

EM Algorithm for Estimation of the Offspring Distribution in Multitype Branching Processes with Terminal Types