Statistical estimation of a growth-fragmentation model observed on a genealogical tree
By Marie Doumic, Marc Hoffmann, Nathalie Krell, L. Robert. 2012
104 citations recorded by the source corpus.
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 growth-fragmentation 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 squared-loss error asymptotically. When the growth rate is assumed to be identical for every cell, we retrieve the classical growth-fragmentation model and our estimator improves on the rate $n^{-s/(2s+3)}$ obtained in \cite{DHRR, DPZ} through indirect observation schemes. Our method is consistently tested numerically and implemented on {\it Escherichia coli} data.
Subfields: Mathematical Physics, Molecular Biology, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/0f42f862a6e107733ca98d1d2d861eff31bf15d2
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In Mathematical Physics
In Molecular Biology
In Statistics and Probability
Citations in the corpus
- Stochastic Models for Structured Populations: Scaling Limits and Long Time Behavior (2015, background): “The asymptotic study of such processes with a non constant rate of division is the object of recent works (see [26, 28, 10] and works in progress).”