Approximate Bayesian Computation in controlled branching processes: the role of summary statistics

TL;DR

This paper explores the use of Approximate Bayesian Computation (ABC) methods in controlled branching processes, proposing effective summary statistics and comparing different algorithms to estimate parameters without explicit likelihood calculations.

Contribution

It introduces tailored summary statistics and evaluates ABC algorithms for controlled branching processes, enhancing likelihood-free Bayesian inference in this context.

Findings

ABC methods approximate posterior distributions effectively.

Sequential Monte Carlo ABC outperforms basic rejection algorithms.

Proposed methods are validated through simulated examples.

Abstract

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.