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Stochastic modeling for population dynamics: simulation and inference - Part 2

By Benoîte de Saporta

Also 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.19604403
  • Cite this video de Saporta, Benoîte (04/02/2020). Stochastic modeling for population dynamics: simulation and inference - Part 2. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19604403
  • URL https://dx.doi.org/10.24350/CIRM.V.19604403

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Bibliography

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  • BRANDEJSKY, Adrien, DE SAPORTA, Benoîte, et DUFOUR, François. Optimal stopping for partially observed piecewise-deterministic Markov processes. Stochastic Processes and their Applications, 2013, vol. 123, no 8, p. 3201-3238. - https://arxiv.org/abs/1207.2886
  • COSTA, O. L. V. et DAVIS, M. H. A. Impulse control of piecewise-deterministic processes. Mathematics of Control, Signals and Systems, 1989, vol. 2, no 3, p. 187-206. - https://doi.org/10.1007/BF02551384
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  • DE SAPORTA, Benoite, DUFOUR, François, et ZHANG, Huilong. Numerical methods for simulation and optimization of piecewise deterministic markov processes. John Wiley & Sons, 2015.
  • GEERAERT, Alizée. Contrôle optimal stochastique des processus de Markov déterministes par morceaux et application à l’optimisation de maintenance. 2017. Thèse de doctorat. Bordeaux. - https://tel.archives-ouvertes.fr/tel-01557969/document
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  • PAGÈS, Gilles, PHAM, Huyên, et PRINTEMS, Jacques. An optimal Markovian quantization algorithm for multi-dimensional stochastic control problems. Stochastics and dynamics, 2004, vol. 4, no 04, p. 501-545. - https://doi.org/10.1142/S0219493704001231
  • PASIN, Chloé. Modélisation et optimisation de la réponse à des vaccins et à des interventions immunothérapeutiques: application au virus Ebola et au VIH. 2018. Thèse de doctorat. Bordeaux. - https://hal.inria.fr/tel-01973077/document
  • PHAM, Huyên, RUNGGALDIER, Wolfgang, et SELLAMI, Afef. Approximation by quantization of the filter process and applications to optimal stopping problems under partial observation. Monte Carlo Methods and Applications mcma, 2005, vol. 11, no 1, p. 57-81. - https://doi.org/10.1515/1569396054027283

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