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On Classes of Equivalence and Identifiability of Age-Dependent Branching Processes

Part of: Markov processes

Published online by Cambridge University Press:  22 February 2016

Rui Chen  and
Ollivier Hyrien
Rui Chen*
Affiliation:
University of Rochester
Ollivier Hyrien*
Affiliation:
University of Rochester
*
∗ Postal address: Department of Biostatistics and Computational Biology, University of Rochester, Rochester, NY 14642, USA.
∗ Postal address: Department of Biostatistics and Computational Biology, University of Rochester, Rochester, NY 14642, USA.
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Abstract

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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.

Keywords

IdentifiabilityBellman-Harris processSevastyanov processSmith-Martin process

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60J85: Applications of branching processes
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 46 , Issue 3 , September 2014 , pp. 704 - 718
Copyright
© Applied Probability Trust 

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