EM algorithm for statistical estimation of two-type branching processes – A focus on the multinomial offspring distribution.

Branching processes form an important and wide subclass of stochastic processes. They have numerous applications in different scientific and practical areas, from biology and cell proliferation through epidemiology, physics and neutral chain reactions to finance and insurance. Many of them involve multitype modeling. Statistical estimation of the process' characteristics is an important issue in their study. The nature of the models require a big amount of data, which is often impossible to be observed, considering only the total population sizes. In order to obtain the maximum likelihood estimators when the information is not sufficient, we use approximation methods. In our study the EM algorithm serves as an effective instrument for calculation of the estimates when a part of data is hidden. We propose examples of two-type branching processes with multinomial offspring distributions and a software implementation of the EM algorithm, illustrated via simulations and computational results. [ABSTRACT FROM AUTHOR]