Laboratoire de Probabilités et Modèles Aléatoires Le Groupe de Travail sur la Longévité a lieu le vendredi de 13h45 à 15h à l'adresse suivante : Université Pierre et Marie Curie - 4 Place Jussieu - 75005 Paris (Métro Jussieu) Couloir 16-26, Salle 113 (1er étage) Organisation : Nicole El Karoui, Sarah Kaakai, Caroline Hillairet, Olivier Lopez. Prochaines Séances
Abstract: We apply matrix analytic methods and branching processes theory to a comparison of female populations in different countries. We show how the same mathematical model allows us to determine characteristics about individual women, such as the distribution of her lifetime, the time until her first and her last daughter, and the number of daughters, as well as to analyze properties of the whole female family generated by a first woman, such as the extinction probability of the family, the distributions of the time until extinction, of the family size at any given time and of the total progeny. In a second part, we consider a class of continuous-time branching processes called Markovian binary trees, in which the individuals lifetime and reproduction epochs are modeled using a transient Markovian arrival process (TMAP). Motivated by datasets on human populations and on the endangered Chatham Island black robin bird species, we develop methods for estimating the parameters of the TMAP, using age-specific global population data and individual demographic data, respectively. Depending on the degree of detail of the available information, a weighted non-linear regression method or a maximum likelihood method is applied. We discuss the optimal choice of the number of phases in the TMAP, and we provide confidence intervals for the model outputs. We gain insights about the conservation of the black robin population through this method of analysis.References: - Hautphenne, S., Massaro, M., & Turner, K. (2017). Fitting Markovian binary trees using global and individual demographic data. arXiv preprint arXiv:1702.04281. - Hautphenne, S., & Latouche, G. (2012). The Markovian binary tree applied to demography. Journal of mathematical biology, 64(7), 1109-1135 |