Predicting extinction or explosion in a Galton–Watson branching process | Zendy

Peter Guttorp | Zendy; Michael D. Perlman | Zendy

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Predicting extinction or explosion in a Galton–Watson branching process

Author(s) -

Peter Guttorp,

Michael D. Perlman

Publication year - 2013

Publication title -

statistical inference for stochastic processes

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.723

H-Index - 20

eISSN - 1572-9311

pISSN - 1387-0874

DOI - 10.1007/s11203-013-9083-0

Subject(s) - branching process , extinction probability , mathematics , lemma (botany) , extinction (optical mineralogy) , simple (philosophy) , branching (polymer chemistry) , statistical physics , statistics , physics , population , epistemology , ecology , philosophy , demography , poaceae , materials science , sociology , population size , optics , composite material , biology

Based on observations \(X_1,\dots ,X_n\) of successive generations of a discrete-parameter Galton–Watson branching process, one wishes to predict whether extinction or explosion will ultimately occur. This problem can be formulated as a simple hypothesis-testing problem to which the Neyman–Pearson Lemma is directly applicable if the extinction probability is known or estimable. If it is not, valid (but conservative) tests still can be obtained.

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