  Multitype branching processes (MTBP) model branching structures, where the
nodes of the resulting tree are objects of different types. One field of
application of such models in biology is in studies of cell proliferation. A
sampling scheme that appears frequently is observing the cell count in several
independent colonies at discrete time points (sometimes only one). Thus, the
process 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 of
every type. This requires an EM-type algorithm to obtain a maximum likelihood
(ML) estimation of the parameters of the branching process. A computational
approach for obtaining such estimation of the offspring distribution is
presented in the class of Markov branching processes with terminal types.
