Parameter estimation in branching processes with almost sure extinction

Braunsteins, Peter; Hautphenne, Sophie; Minuesa, Carmen

doi:10.3150/21-bej1332

Cited by 2 publications

(1 citation statement)

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“…We refer to the latter value as the carrying capacity of the population, denoted as K (see [3]). Population-size dependent branching processes (PSDBPs) are often used to model these kind of data (see, for instance, [4], [12], or [15] and references therein). The PSDBP is a modification of a BGW process.…”

Section: Real Data Examplesmentioning

confidence: 99%

Approximate Bayesian computation approach on the maximal offspring and parameters in controlled branching processes

González

Minuesa

Puerto

2022

Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat.

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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 twofold. 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.

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