  Controlled branching processes are stochastic growth population models in
which the number of individuals with reproductive capacity in each generation
is controlled by a random control function. The purpose of this work is to
examine the Approximate Bayesian Computation (ABC) methods and to propose
appropriate summary statistics for them in the context of these processes. This
methodology enables to approximate the posterior distribution of the parameters
of interest satisfactorily without explicit likelihood calculations and under a
minimal set of assumptions. In particular, the tolerance rejection algorithm,
the sequential Monte Carlo ABC algorithm, and a post-sampling correction method
based on local-linear regression are provided. The accuracy of the proposed
methods are illustrated and compared with a "likelihood free" Markov chain
Monte Carlo technique by the way of a simulated example developed with the
statistical software R.
