LJKProbability & Statistics Seminar

On Thursday October 3 2013 at 14h00 in Salle 1  Tour IRMA

Seminary of Marc HOFFMANN (Université Paris Dauphine)

Statistical estimation of a growthfragmentation model observed on a genealogical tree

Summary

We model the growth of a cell population by a piecewise deterministic Markov branching tree. Each cell splits into two offsprings at a division rate B(x) that depends on its size x. The size of each cell grows exponentially in time, at a rate that varies for each individual. We show that the mean empirical measure of the model satisfies a growthfragmentation type equation if structured in both size and growth rate as state variables. We construct a nonparametric estimator of the division rate B(x) based on the observation of the population over different sampling schemes of size n on the genealogical tree. Our estimator nearly achieves the rate n^{s/(2s+1)} in squaredloss error asymptotically. When the growth rate is assumed to be identical for every cell, we retrieve the classical growthfragmentation model and our estimator improves on the rate n^{s/(2s+3)} obtained in a related framework through indirect observation schemes. Our method is consistently tested numerically and implemented on Escherichia coli data.
