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# Documents  65C35 | enregistrements trouvés : 8

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## Island filters for inference on metapopulation dynamics Ionides, Edward | CIRM H

Multi angle

Research talks;Probability and Statistics

Low-dimensional compartment models for biological systems can be fitted to time series data using Monte Carlo particle filter methods. As dimension increases, for example when analyzing a collection of spatially coupled populations, particle filter methods rapidly degenerate. We show that many independent Monte Carlo calculations, each of which does not attempt to solve the filtering problem, can be combined to give a global filtering solution with favorable theoretical scaling properties under a weak coupling condition. The independent Monte Carlo calculations are called islands, and the operation carried out on each island is called adapted simulation, so the complete algorithm is called an adapted simulation island filter. We demonstrate this methodology and some related algorithms on a model for measles transmission within and between cities. Low-dimensional compartment models for biological systems can be fitted to time series data using Monte Carlo particle filter methods. As dimension increases, for example when analyzing a collection of spatially coupled populations, particle filter methods rapidly degenerate. We show that many independent Monte Carlo calculations, each of which does not attempt to solve the filtering problem, can be combined to give a global filtering solution ...

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## Particle algorithm for McKean SDE: a short review on numerical analysis Bossy, Mireille | CIRM H

Multi angle

Research schools;Probability and Statistics;Numerical Analysis and Scientific Computing

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## Projected particle methods for solving McKean Vlasov SDEs Belomestny, Denis | CIRM H

Multi angle

Research talks;Numerical Analysis and Scientific Computing

We propose a novel projection-based particle method for solving the McKean-Vlasov stochastic differential equations. Our approach is based on a projection-type estimation of the marginal density of the solution in each time step.
The projection-based particle method leads in many situation to a significant reduction of numerical complexity compared to the widely used kernel density estimation algorithms.
We derive strong convergence rates and rates of density estimation. The convergence analysis in the case of linearly growing coefficients turns out to be rather challenging and requires some new type of averaging technique.
This case is exemplified by explicit solutions to a class of McKean-Vlasov equations with affine drift.
The performance of the proposed algorithm is illustrated by several numerical examples.
We propose a novel projection-based particle method for solving the McKean-Vlasov stochastic differential equations. Our approach is based on a projection-type estimation of the marginal density of the solution in each time step.
The projection-based particle method leads in many situation to a significant reduction of numerical complexity compared to the widely used kernel density estimation algorithms.
We derive strong convergence rates and ...

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## Rare event simulation for molecular dynamics Guyader, Arnaud | CIRM H

Multi angle

Research talks;Numerical Analysis and Scientific Computing;Probability and Statistics

This talk is devoted to the presentation of algorithms for simulating rare events in a molecular dynamics context, e.g., the simulation of reactive paths. We will consider $\mathbb{R}^d$ as the space of configurations for a given system, where the probability of a specific configuration is given by a Gibbs measure depending on a temperature parameter. The dynamics of the system is given by an overdamped Langevin (or gradient) equation. The problem is to find how the system can evolve from a local minimum of the potential to another, following the above dynamics. After a brief overview of classical Monte Carlo methods, we will expose recent results on adaptive multilevel splitting techniques. This talk is devoted to the presentation of algorithms for simulating rare events in a molecular dynamics context, e.g., the simulation of reactive paths. We will consider $\mathbb{R}^d$ as the space of configurations for a given system, where the probability of a specific configuration is given by a Gibbs measure depending on a temperature parameter. The dynamics of the system is given by an overdamped Langevin (or gradient) equation. The ...

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## Splitting algorithm for nested events Goudenège, Ludovic | CIRM H

Multi angle

Research talks;Probability and Statistics;Numerical Analysis and Scientific Computing

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.
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 ...

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## Explorations in Monte Carlo methods Shonkwiler, Ronald W. ; Mendivil, Franklin | Springer 2009

Ouvrage

- xii; 243 p.
ISBN 978-0-387-87836-2

Localisation : Ouvrage RdC (SHON)

simulation informatique # probabilités # distribution # algorithme # optimisation mathématique # processus stochastique # méthode de Monte-Carlo # théorie des jeux # simulation numérique

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## Méthodes de Monte-Carlo avec R Robert, Christian P. ; Casella, George ; Robert, Joachim ; Ryder, Robin ; Arbel, Julyan ; Jacob, Pierre ; Plessis, Brigitte | Springer 2011

Ouvrage

- xv; 256 p.
ISBN 978-2-8178-0180-3

Pratique R

Localisation : Ouvrage RdC (ROBE)

méthode de Monte-Carlo # langage de programmation R # simulation statistique # analyse bayésienne

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## Monte-Carlo methods and stochastic processes:from linear to non-linear Gobet, Emmanuel | CRC Press 2016

Ouvrage

- xxv; 309 p.
ISBN 978-1-4987-4622-9

Localisation : Ouvrage RdC (GOBE)

méthode de Monte-Carlo # processus stochastique # méthode de simulation # convergence d'algorithmes # équation différentielle stochastique # dynamique non linéaire

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