Statistical study of asymmetry in cell lineage data

Benoîte de Saporta; Anne Gégout Petit; Laurence Marsalle

hal-00702359, version 1

Statistical study of asymmetry in cell lineage data

Benoîte de Saporta ^1, 2, 3, Anne Gégout Petit ^1, 2, Laurence Marsalle ⁴

(22/05/2012)

Abstract: This paper proposes a rigorous methodology to study cell division data consisting in several observed genealogical trees. We model the data by an asymmetric bifurcating autoregressive (BAR) process and take into account possibly missing observations by modeling the genealogies with a two-type Galton Watson (GW) process. Our inference is based on several lineages, i.e. independent and identically distributed replicas of the coupled BAR and GW processes, corresponding to several data trees obtained in similar experimental conditions. We propose a least-squares estimator of the unknown parameters of the BAR process and an estimator of the parameters of the GW process, give their asymptotic properties and derive symmetry tests. Our results are applied on real data of Escherichia coli division.

1: Institut de Mathématiques de Bordeaux (IMB)
CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II
2: CQFD (INRIA Bordeaux - Sud-Ouest)
INRIA – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II – CNRS : UMR5251
3: Groupe de Recherche en Economie Théorique et Appliquée (GREThA)
CNRS : UMR5113 – Université Montesquieu - Bordeaux IV
4: Laboratoire Paul Painlevé (LPP)
CNRS : UMR8524 – Université Lille I - Sciences et technologies

hal-00702359, version 1
http://hal.archives-ouvertes.fr/hal-00702359
oai:hal.archives-ouvertes.fr:hal-00702359
From: Benoîte De Saporta <>
Submitted on: Wednesday, 30 May 2012 09:39:18
Updated on: Wednesday, 30 May 2012 09:39:18

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arXiv: 1205.4840

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