Geodesic
Using Inside-Outside Algorithm for Estimation of the Offspring Distribution in Multitype Branching Processes
Serdica Journal of Computing, Tome 4 (2010) no. 4, pp. 463-474.

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Multitype branching processes (MTBP) model branching structures, where the nodes of the resulting tree are particles of different types. Usually such a process is not observable in the sense of the whole tree, but only as the “generation” at a given moment in time, which consists of the number of particles of every type. This requires an EM-type algorithm to obtain a maximum likelihood (ML) estimate of the parameters of the branching process. Using a version of the inside-outside algorithm for stochastic context-free grammars (SCFG), such an estimate could be obtained for the offspring distribution of the process.
Keywords: Multitype Branching Processes, Offspring Distribution, Maximum Likelihood Estimation, Expectation Maximization, Stochastic Context-Free Grammars, Inside-Outside Algorithm 
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Daskalova, Nina. Using Inside-Outside Algorithm for Estimation of the Offspring Distribution in Multitype Branching Processes. Serdica Journal of Computing, Tome 4 (2010) no. 4, pp. 463-474. http://geodesic.mathdoc.fr/item/SJC_2010_4_4_a4/