arXiv subjects

C. Minuesa

Publications and source records attributed to C. Minuesa.

3 recordsLinked to original sources

arXiv2019

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

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.

stat.ME↗

arXiv2018

Robust estimation in controlled branching processes: Bayesian estimators via disparities

This paper is concerned with Bayesian inferential methods for data from controlled branching processes that account for model robustness through the use of disparities. Under regularity conditions, we establish that estimators built on disparity-based posterior, such as expectation and maximum a posteriori estimates, are consistent and efficient under the posited model. Additionally, we show that the estimates are robust to model misspecification and presence of aberrant outliers. To this end, we develop several fundamental ideas relating minimum disparity estimators to Bayesian estimators built on the disparity-based posterior, for dependent tree-structured data. We illustrate the methodology through a simulated example and apply our methods to a real data set from cell kinetics.

stat.ME↗

arXiv2015

Maximum likelihood estimation and Expectation-Maximization algorithm for controlled branching processes

The controlled branching process is a generalization of the classical Bienaymé-Galton-Watson branching process. It is a useful model for describing the evolution of populations in which the population size at each generation needs to be controlled. The maximum likelihood estimation of the parameters of interest for this process is addressed under various sample schemes. Firstly, assuming that the entire family tree can be observed, the corresponding estimators are obtained and their asymptotic properties investigated. Secondly, since in practice it is not usual to observe such a sample, the maximum likelihood estimation is initially considered using the sample given by the total number of individuals and progenitors of each generation, and then using the sample given by only the generation sizes. Expectation-maximization algorithms are developed to address these problems as incomplete data estimation problems. The accuracy of the procedures is illustrated by means of a simulated example.

math.ST↗