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# Documents  60J22 | enregistrements trouvés : 7

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## Monte Carlo and quasi-Monte Carlo methods 2010.Selected papers based on the presentations at the 9th international conference on Monte Carlo and quasi Monte Carlo in scientific computing (MCQMC 2010)Warsaw # august 15-20, 2010 Plaskota, Leszek ; Wozniakowski, Henryk | Springer 2012

Congrès

- xii; 732 p.
ISBN 978-3-642-27439-8

Springer proceedings in mathematics & statistics

Localisation : Colloque 1er étage (WARS)

méthode de Monte Carlo # méthode de quasi-Monte Carlo # statistique en grande dimension # finance # analyse numérique # probabilités # chaîne de Markov

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## An introduction to particle filters Chopin, Nicolas | CIRM H

Multi angle

Research School

This course will give a gentle introduction to SMC (Sequential Monte Carlo algorithms):
• motivation: state-space (hidden Markov) models, sequential analysis of such models; non-sequential problems that may be tackled using SMC.
• Formalism: Markov kernels, Feynman-Kac distributions.
• Monte Carlo tricks: importance sampling and resampling
• standard particle filters: bootstrap, guided, auxiliary
• maximum likelihood estimation of state-stace models
• Bayesian estimation of these models: PMCMC, SMC$^2$.
This course will give a gentle introduction to SMC (Sequential Monte Carlo algorithms):
• motivation: state-space (hidden Markov) models, sequential analysis of such models; non-sequential problems that may be tackled using SMC.
• Formalism: Markov kernels, Feynman-Kac distributions.
• Monte Carlo tricks: importance sampling and resampling
• standard particle filters: bootstrap, guided, auxiliary
• maximum likelihood estimation of state-stace ...

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

Multi angle

Research talks;Probability and Statistics

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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## The Metropolis Hastings algorithm: introduction and optimal scaling of the transient phase Jourdain, Benjamin | CIRM H

Multi angle

Research schools;Probability and Statistics

We first introduce the Metropolis-Hastings algorithm. We then consider the Random Walk Metropolis algorithm on $R^n$ with Gaussian proposals, and when the target probability measure is the $n$-fold product of a one dimensional law. It is well-known that, in the limit $n$ tends to infinity, starting at equilibrium and for an appropriate scaling of the variance and of the timescale as a function of the dimension $n$, a diffusive limit is obtained for each component of the Markov chain. We generalize this result when the initial distribution is not the target probability measure. The obtained diffusive limit is the solution to a stochastic differential equation nonlinear in the sense of McKean. We prove convergence to equilibrium for this equation. We discuss practical counterparts in order to optimize the variance of the proposal distribution to accelerate convergence to equilibrium. Our analysis confirms the interest of the constant acceptance rate strategy (with acceptance rate between 1/4 and 1/3). We first introduce the Metropolis-Hastings algorithm. We then consider the Random Walk Metropolis algorithm on $R^n$ with Gaussian proposals, and when the target probability measure is the $n$-fold product of a one dimensional law. It is well-known that, in the limit $n$ tends to infinity, starting at equilibrium and for an appropriate scaling of the variance and of the timescale as a function of the dimension $n$, a diffusive limit is obtained ...

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## Markov chains: analytic and Monte Carlo computations Graham, Carl | John Wiley & Sons, LTD;Dunod 2014

Ouvrage

- xvi; 232 p.
ISBN 978-1-118-51707-9

Wiley series in probability and statistics

Localisation : Ouvrage RdC (GRAH)

processus de Markov # méthode de Monte Carlo # chaîne de Markov # analyse numérique

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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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## Finite Markov chains and algorithmic applications Häggström, Olle | Cambridge University Press 2002

Ouvrage

- 114 p.
ISBN 978-0-521-89001-4

London mathematical society student texts , 0052

Localisation : Collection 1er étage

probabilité # chaîne de Markov # méthode de Monte Carlo # simulation parfaite # algorithme de Propp-Wilson # modèle d'Ising # problème du "voyageur de commerce"

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