Detection of cellular aging in a Galton-Watson process
By Jean-François Delmas, Laurence Marsalle. 2008
65 citations recorded by the source corpus.
We consider the bifurcating Markov chain model introduced by Guyon to detect cellular aging from cell lineage. To take into account the possibility for a cell to die, we use an underlying super-critical binary Galton-Watson process to describe the evolution of the cell lineage. We give in this more general framework a weak law of large number, an invariance principle and thus fluctuation results for the average over all individuals in a given generation, or up to a given generation. We also prove that the fluctuations over each generation are independent. Then we present the natural modifications of the tests given by Guyon in cellular aging detection within the particular case of the auto-regressive model.
Subfields: Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/9efe25150abeacb79025a6eaf692c20fd2fdc549
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In Mathematical Physics
In Statistics and Probability
Citations in the corpus
- Limit theorems for Markov processes indexed by continuous time Galton--Watson trees (2009, methodology): “give 10 a more important weight to branches where there have been more divisions and more children since the proportion of the corresponding offspring will be higher. Our pathwise approach generalizes [17] (discrete time) and [7] (continuous time Yule process). As mentioned in the introduction, this ”
- Limit theorems for some branching measure-valued processes (2011, background): “A long time behaviour for a similar discrete model is developed in [18].”