Advances in Applied Probability

On classes of equivalence and identifiability of age-dependent branching processes

Rui Chen and Ollivier Hyrien

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Age-dependent branching processes are increasingly used in analyses of biological data. Despite being central to most statistical procedures, the identifiability of these models has not been studied. In this paper we partition a family of age-dependent branching processes into equivalence classes over which the distribution of the population size remains identical. This result can be used to study identifiability of the offspring and lifespan distributions for parametric families of branching processes. For example, we identify classes of Markov processes that are not identifiable. We show that age-dependent processes with (nonexponential) gamma-distributed lifespans are identifiable and that Smith-Martin processes are not always identifiable.

Article information

Adv. in Appl. Probab., Volume 46, Number 3 (2014), 704-718.

First available in Project Euclid: 29 August 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60J85: Applications of branching processes [See also 92Dxx]

Identifiability Bellman-Harris process Sevastyanov process Smith-Martin process


Chen, Rui; Hyrien, Ollivier. On classes of equivalence and identifiability of age-dependent branching processes. Adv. in Appl. Probab. 46 (2014), no. 3, 704--718. doi:10.1239/aap/1409319556.

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