Advances in Applied Probability

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

Rui Chen and Ollivier Hyrien

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Abstract

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

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

Dates
First available in Project Euclid: 29 August 2014

Permanent link to this document
https://projecteuclid.org/euclid.aap/1409319556

Digital Object Identifier
doi:10.1239/aap/1409319556

Mathematical Reviews number (MathSciNet)
MR3254338

Zentralblatt MATH identifier
1307.60117

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

Keywords
Identifiability Bellman-Harris process Sevastyanov process Smith-Martin process

Citation

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. https://projecteuclid.org/euclid.aap/1409319556


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