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H 1 Stochastic modeling for population dynamics: simulation and inference - Part 1

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    Résumé : 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.

    Keywords : Markov process; numeric probabilities; stochastic control; applications to biology

    Codes MSC :
    60Jxx - Markov processes
    90Cxx - Mathematical programming, See also {49Mxx, 65Kxx}
    92Bxx - Mathematical biology in general

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 21/02/2020
      Date de captation : 03/02/2020
      Collection : Research School ; Probability and Statistics
      Format : MP4
      Durée : 01:41:31
      Domaine : Probability & Statistics
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2020-02-03_Saporta_Part1.mp4

    Informations sur la rencontre

    Nom de la rencontre : Thematic Month Week 1: PDE and Probability for Biology / Mois thématique Semaine 1 : EDP et probabilité pour la biologie
    Dates : 03/02/2020 - 07/02/2020
    Année de la rencontre : 2020
    URL Congrès : https://conferences.cirm-math.fr/2301.html

    Citation Data

    DOI : 10.24350/CIRM.V.19604303
    Cite this video as: (2020). Stochastic modeling for population dynamics: simulation and inference - Part 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19604303
    URI : http://dx.doi.org/10.24350/CIRM.V.19604303


    Voir aussi

    Bibliographie

    1. BAUERLE, Nicole et LANGE, Dirk. Optimal Control of Partially Observable Piecewise Deterministic Markov Processes. SIAM Journal on Control and Optimization, 2018, vol. 56, no 2, p. 1441-1462. - https://arxiv.org/abs/1706.09142

    2. 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

    3. 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

    4. DAVIS, M. H. A. Markov models and optimization. Monographs on Statistics & Applied Probability, vol. 49, Chapman & Hall / CRC, 1993. -

    5. DE SAPORTA, Benoite, DUFOUR, François, et ZHANG, Huilong. Numerical methods for simulation and optimization of piecewise deterministic markov processes. John Wiley & Sons, 2015. -

    6. 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

    7. PAGÈS, Gilles. A space quantization method for numerical integration. Journal of computational and applied mathematics, 1998, vol. 89, no 1, p. 1-38. - https://doi.org/10.1016/S0377-0427(97)00190-8

    8. 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

    9. 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

    10. 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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