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Stochastic modeling for population dynamics: simulation and inference - Part 3

By Benoîte de Saporta

Appears in collection : Thematic Month Week 1: PDE and Probability for Biology / Mois thématique Semaine 1 : EDP et probabilité pour la biologie

The aim of this course is to present some examples of stochastic models suitable for population dynamics. The first part will introduce a class of continuous time models called piecewise deterministic Markov processes (PDMPs). Their trajectories are deterministic with jumps at random times. They are especially suitable to model phenomena with different time scales: a fast time-sacla corresponding to the deterministic behaviour and a slow time-scale corresponding to the jumps. I'll present different biological systems that can be modelled by PDMPs, explain how they can be simulated. The second part will focus on random models for cell division when the whole branching population is taken into account. I'll present two data sets from biological experiments trying to determine whether cell division is symmetric or not. I'll explain how statistic tools can help answer this question.

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Citation data

  • DOI 10.24350/CIRM.V.19604503
  • Cite this video de Saporta, Benoîte (04/02/2020). Stochastic modeling for population dynamics: simulation and inference - Part 3. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19604503
  • URL https://dx.doi.org/10.24350/CIRM.V.19604503

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Bibliography

  • COWAN, Richard et STAUDTE, Robert. The bifurcating autoregression model in cell lineage studies. Biometrics, 1986, p. 769-783. - http://dx.doi.org/10.2307/2530692
  • STEWART, Eric J., MADDEN, Richard, PAUL, Gregory, et al. Aging and death in an organism that reproduces by morphologically symmetric division. PLoS biology, 2005, vol. 3, no 2. - https://doi.org/10.1371/journal.pbio.0030045
  • GUYON, Julien, et al. Limit theorems for bifurcating Markov chains. Application to the detection of cellular aging. The Annals of Applied Probability, 2007, vol. 17, no 5/6, p. 1538-1569. - https://arxiv.org/abs/0710.5434
  • GÉGOUT-PETIT, Anne, DE SAPORTA, Benoîte, et BERCU, Bernard. Asymptotic Analysis for Bifurcating Autoregressive Processes via a martingale approach. - https://arxiv.org/abs/0807.0528
  • DELMAS, Jean-François et MARSALLE, Laurence. Detection of cellular aging in a Galton–Watson process. Stochastic Processes and their Applications, 2010, vol. 120, no 12, p. 2495-2519. - https://dx.doi.org/10.1016/j.spa.2010.07.002
  • DE SAPORTA, Benoîte, GÉGOUT-PETIT, Anne, MARSALLE, Laurence, et al. Parameters estimation for asymmetric bifurcating autoregressive processes with missing data. Electronic Journal of Statistics, 2011, vol. 5, p. 1313-1353. - https://dx.doi.org/10.1214/11-EJS643
  • WANG, Ping, ROBERT, Lydia, PELLETIER, James, et al. Robust growth of Escherichia coli. Current biology, 2010, vol. 20, no 12, p. 1099-1103. - https://doi.org/10.1016/j.cub.2010.04.045
  • DE SAPORTA, Benoîte, GÉGOUT-PETIT, Anne, et MARSALLE, Laurence. Asymmetry tests for bifurcating auto-regressive processes with missing data. Statistics & Probability Letters, 2012, vol. 82, no 7, p. 1439-1444. - https://arxiv.org/abs/1112.3745
  • DE SAPORTA, Benoîte, GÉGOUT-PETIT, Anne, et MARSALLE, Laurence. Random coefficients bifurcating autoregressive processes. ESAIM: Probability and Statistics, 2014, vol. 18, p. 365-399. - https://arxiv.org/abs/1205.3658
  • DE SAPORTA, Benoíte, GÉGOUT-PETIT, Anne, et MARSALLE, Laurence. Statistical study of asymmetry in cell lineage data. Computational Statistics & Data Analysis, 2014, vol. 69, p. 15-39. - https://dx.doi.org/10.1016/j.csda.2013.07.025
  • DELYON, Bernard, DE SAPORTA, Benoîte, KRELL, Nathalie, et al. Investigation of asymmetry in E. coli growth rate. arXiv preprint arXiv:1509.05226, 2015. - https://arxiv.org/abs/1509.05226

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