University of Washington - Statistics
For a Galton-Watson branching process, extinction is certain if the offspring mean $\mu\le1$ whereas explosion is possible (but not certain) if $\mu>1$; discriminating between these two possibilities is a hypothesis-testing problem for the parameter $\mu$. However, if it is assumed or known that $\mu>1$ then deciding whether extinction or explosion will occur for a single realization of the process is a prediction problem, which can be formulated as a similar but distinct testing problem by considering the conditional distributions of the process given extinction and explosion respectively. For power series offspring distributions, parametric tests are presented for both problems and illustrated with several examples.
This is joint work with Peter Guttorp