Using Inside-Outside Algorithm for Estimation of the Offspring Distribution in Multitype Branching Processes

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.

Em Estimation of the Offspring Distribution in Mutitype Branching Processes - a Model in Cell Kinetics

2000 Mathematics Subject Classification: 60J80, 60J85, 62P10, 92D25.

Estimation of the Offspring and Immigration Mean Vectors for Bisexual Branching Processes with Immigration of Females and Males

2000 Mathematics Subject Classification: 60J80, 62M05.

Offspring Mean Estimators in Branching Processes with Immigration

2000 Mathematics Subject Classification: 60J80.

Revisiting Offspring Maxima in Branching Processes

2000 Mathematics Subject Classification: 60J80; 60G70.

Estimation of the Offspring Mean in a General Single-Type Size-Dependent Branching Process

2000 Mathematics Subject Classification: 60J80, 62F12, 62P10