Model choice and parameter inference in controlled branching processes

TL;DR

This paper introduces a likelihood-free Bayesian approach using ABC algorithms to estimate parameters of controlled branching processes without prior knowledge of offspring limits, demonstrated on simulated and real population data.

Contribution

It presents a novel ABC-based methodology for parameter inference in CBPs that does not require explicit likelihood calculations or prior offspring limits.

Findings

Accurate parameter estimation demonstrated on simulated data.

Effective model choice for population growth scenarios.

Application to real datasets with logistic growth models.

Abstract

Our purpose is to estimate the posterior distribution of the parameters of interest for controlled branching processes (CBPs) without prior knowledge of the maximum number of offspring that an individual can give birth to and without explicit likelihood calculations. We consider that only the population sizes at each generation and at least the number of progenitors of the last generation are observed, but the number of offspring produced by any individual at any generation is unknown. The proposed approach is two-fold. Firstly, to estimate the maximum progeny per individual we make use of an approximate Bayesian computation (ABC) algorithm for model choice and based on sequential importance sampling with the raw data. Secondly, given such an estimate and taking advantage of the simulated values of the previous stage, we approximate the posterior distribution of the main parameters of a CBP by applying the rejection ABC algorithm with an appropriate summary statistic and a post-processing adjustment. The accuracy of the proposed method is illustrated by means of simulated examples developed with the statistical software R. Moreover, we apply the methodology to two real datasets describing populations with logistic growth. To this end, different population growth models based on CBPs are proposed for the first time.