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Splitting algorithm for nested events
Multi angle
Authors : Goudenège, Ludovic (Author of the conference)
CIRM (Publisher )
60J22 - Computational methods in Markov chains
65C05 - Monte Carlo methods
65C40 - Computational Markov chains (numerical analysis)
65C35 - Stochastic particle methods (numerical analysis)
Additional resources :
http://www.lpma-paris.fr/pageperso/benezet/CEMRACS2017/Goudenege.pdf
CIRM (Publisher )
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Abstract :
Consider a problem of Markovian trajectories of particles for which you are trying to estimate the probability of a event.
Under the assumption that you can represent this event as the last event of a nested sequence of events, it is possible to design a splitting algorithm to estimate the probability of the last event in an efficient way. Moreover you can obtain a sequence of trajectories which realize this particular event, giving access to statistical representation of quantities conditionally to realize the event.
In this talk I will present the "Adaptive Multilevel Splitting" algorithm and its application to various toy models. I will explain why it creates an unbiased estimator of a probability, and I will give results obtained from numerical simulations.
MSC Codes : Under the assumption that you can represent this event as the last event of a nested sequence of events, it is possible to design a splitting algorithm to estimate the probability of the last event in an efficient way. Moreover you can obtain a sequence of trajectories which realize this particular event, giving access to statistical representation of quantities conditionally to realize the event.
In this talk I will present the "Adaptive Multilevel Splitting" algorithm and its application to various toy models. I will explain why it creates an unbiased estimator of a probability, and I will give results obtained from numerical simulations.
60J22 - Computational methods in Markov chains
65C05 - Monte Carlo methods
65C40 - Computational Markov chains (numerical analysis)
65C35 - Stochastic particle methods (numerical analysis)
Additional resources :
http://www.lpma-paris.fr/pageperso/benezet/CEMRACS2017/Goudenege.pdf
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 03/08/17 Conference Date : 01/08/17 Subseries : Research talks arXiv category : Probability ; Numerical Analysis Mathematical Area(s) : Numerical Analysis & Scientific Computing ; Probability & Statistics Format : MP4 (.mp4) - HD Video Time : 00:43:13 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2017-08-01_Goudenege.mp4 
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Information on the Event
Event Title : CEMRACS: Numerical methods for stochastic models: control, uncertainty quantification, mean-field / CEMRACS : Méthodes numériques pour équations stochastiques : contrôle, incertitude, champ moyenEvent Organizers : Bouchard, Bruno ; Chassagneux, Jean-François ; Delarue, François ; Gobet, Emmanuel ; Lelong, Jérôme Dates : 17/07/17 - 25/08/17 Event Year : 2017 Event URL : http://conferences.cirm-math.fr/1556.html
Citation Data
DOI : 10.24350/CIRM.V.19204103Cite this video as: Goudenège, Ludovic (2017). Splitting algorithm for nested events. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19204103 URI : http://dx.doi.org/10.24350/CIRM.V.19204103 |
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Bibliography
- Bréhier, C.-E., Gazeau, M., Goudenège, L., Lelièvre, T., & Rousset, M. (2016). Unbiasedness of some generalized adaptive multilevel splitting algorithms. The Annals of Applied Probability, 26(6), 3559-3601 - http://dx.doi.org/10.1214/16-AAP1185
