Bayesian inference for controlled branching processes through MCMC and ABC methodologies

• Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2013-09, Vol.107 (2), p.459-473
• Main Authors: González, Miguel, Gutiérrez, Cristina, Martínez, Rodrigo, del Puerto, Inés M.
• Format: Article
• Language: English
• Subjects: Applications of Mathematics; Approximation; Mathematical and Computational Physics; Mathematics; Mathematics and Statistics; Original Paper; Theoretical
• ISSN: 1578-7303; 1579-1505
• DOI: 10.1007/s13398-012-0072-8

The controlled branching process (CBP) is a generalization of the classical Bienaymé–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.