Journal
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
Volume 107, Issue 2, Pages 459-473Publisher
SPRINGER-VERLAG ITALIA SRL
DOI: 10.1007/s13398-012-0072-8
Keywords
Controlled branching process; Bayesian inference; Gibbs sampler; Approximate Bayesian computation; Non-parametric
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Funding
- Ministerio de Ciencia e Innovacion
- FEDER [MTM2009-13248]
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The controlled branching process (CBP) is a generalization of the classical Bienaym,-Galton-Watson branching process, and, in the terminology of population dynamics, is used to describe the evolution of populations in which a control of the population size at each generation is needed. In this work, we deal with the problem of estimating the offspring distribution and its main parameters for a CBP with a deterministic control function assuming that the only observable data are the total number of individuals in each generation. We tackle the problem from a Bayesian perspective in a non parametric context. We consider a Markov chain Monte Carlo (MCMC) method, in particular the Gibbs sampler and approximate Bayesian computation (ABC) methodology. The first is a data imputation method and the second relies on numerical simulations. Through a simulated experiment we evaluate the accuracy of the MCMC and ABC techniques and compare their performances.
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