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

TL;DR

This paper develops an EM algorithm to estimate offspring distributions in multitype branching processes with terminal types, useful for biological cell proliferation studies where only partial observations are available.

Contribution

It introduces a computational EM-based method for maximum likelihood estimation in Markov branching processes with terminal types, addressing partial observation challenges.

Findings

Provides an EM algorithm tailored for multitype branching processes with terminal types.

Enables ML estimation from partial, generation-based observations.

Applicable to biological studies of cell proliferation.

Abstract

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.