We consider two-type branching stochastic processes with offspring distributions from the power series distribution family. The estimation of the individual parameters is an important part of the statistical inference for branching processes. Models of estimation of multitype branching processes require a large amount of data that cannot always be observed and the the size of the population is often insufficient. The use of approximation methods like the machine learning approach to parameter estimation, allows us to obtain an algorithmic estimation in the presence of hidden data. This gives us a motivation to approach the parametric statistical estimation in the multitype branching setting using machine learning algorithms. We consider a Hamiltonian Monte Carlo algorithm to algorithmically estimate the parameters of the individual distribution of a two-type branching process and compare it to the Gibbs sampler. As a special case we consider the branching process with a multivariate Poisson offspring distribution. Examples are provided, as well as a software implementation, illustrated by simulations and computational results in Python.
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