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# Documents  60G09 | enregistrements trouvés : 10

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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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## Centered partition processes: lumping versus splitting in sparse health data Herring, Amy | CIRM H

Multi angle

Research talks

In many health studies, interest often lies in assessing health effects on a large set of outcomes or specific outcome subtypes, which may be sparsely observed, even in big data settings. For example, while the overall prevalence of birth defects is not low, the vast heterogeneity in types of congenital malformations leads to challenges in estimation for sparse groups. However, lumping small groups together to facilitate estimation is often controversial and may have limited scientific support.
There is a very rich literature proposing Bayesian approaches for clustering starting with a prior probability distribution on partitions. Most approaches assume exchangeability, leading to simple representations in terms of Exchangeable Partition Probability Functions (EPPF). Gibbs-type priors encompass a broad class of such cases, including Dirichlet and Pitman-Yor processes. Even though there have been some proposals to relax the exchangeability assumption, allowing covariate-dependence and partial exchangeability, limited consideration has been given on how to include concrete prior knowledge on the partition. We wish to cluster birth defects into groups to facilitate estimation, and we have prior knowledge of an initial clustering provided by experts. As a general approach for including such prior knowledge, we propose a Centered Partition (CP) process that modifies the EPPF to favor partitions close to an initial one. Some properties of the CP prior are described, a general algorithm for posterior computation is developed, and we illustrate the methodology through simulation examples and an application to the motivating epidemiology study of birth defects.
In many health studies, interest often lies in assessing health effects on a large set of outcomes or specific outcome subtypes, which may be sparsely observed, even in big data settings. For example, while the overall prevalence of birth defects is not low, the vast heterogeneity in types of congenital malformations leads to challenges in estimation for sparse groups. However, lumping small groups together to facilitate estimation is often ...

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## Martingale limit theory and its application Hall, P. ; Heyde, C. C. | Academic Press 1980

Ouvrage

- 308 p.
ISBN 978-0-12-319350-6

Probability and mathematical statistics

Localisation : Ouvrage RdC (HALL)

approximation stochastique # crible aléatoire de Hawkins # estimation qde paramètre # inégalité # loi des grands nombres # loi du logarithme itéré # martingale d'approximation # processus stationaire # processus stochastique # suite échangeable # théorie limite des martingales # théorème de convergence des martingales # théorème limite central

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## Combinatorial methods in the theory of stochastic processes Takacs, Lajos | John Wiley And Sons 1967

Ouvrage

- 262 p.

Wiley series in probability and mathematical statistics

Localisation : Ouvrage RdC (TAKA)

distribution # fluctuation # méthode combinatoire # processus stochastique # variable aléatoire

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## Studies in inductive logic and probability. Vol. II Jeffrey, R. C. | University Of California Press 1980

Ouvrage

- 305 p.
ISBN 978-0-520-03826-4

Localisation : Ouvrage RdC (Stud)

collection des papiers # logique inductive # probabilité

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## Logique du probable :démarche bayesienne et rationalité Suppes, Patrick | Flammarion 1981

Ouvrage

- 136 p.
ISBN 978-2-08-211130-0

Nouvelle bibliothèque scientifique

Localisation : Ouvrage RdC (SUPP)

apprentissage # approximation # causalité # limite de la rationalité # modèle concurent # probabilité

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## Probability theoryindependence, interchangeability, martingales Chow, Yuan Shih ; Teicher, Henry | Springer 1997

Ouvrage

- 488 p.
ISBN 978-0-387-98228-1

Springer texts in statistics

Localisation : Ouvrage RdC (CHOW)

espace de probabilité # fonction caractéristique # fonction de distribution # fondement # inférence paramétrique # interchangeabilité # martingale # mesure théorique # processus stochastique # statistique # théorie des probabilités # théorème centrale limite # variable aléatoire

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## Random fragmentation and coagulation processes Bertoin, Jean | Cambridge University Press 2006

Ouvrage

- 280 p.
ISBN 978-0-521-86728-3

Cambridge studies in advanced mathematics , 0102

Localisation : Ouvrage RdC (BERT)

probabilités # probabilités combinatoriales # processus autosimilaire # théorème limite fort # processus de Markov # processus de branchement # arbre aléatoire # mesure de Poisson # limite hydrodynamique # équation de Smoluchowski

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## The Sherrington-Kirkpatrick model Panchenko, Dmitry | Springer 2013

Ouvrage

- xii; 156 p.
ISBN 978-1-4614-6288-0

Springer monographs in mathematics

Localisation : Ouvrage RdC (PANC)

formule de Parisi # mesure de Gibbs # verre de spin

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## Recueil de modèles aléatoires Chafaï, Djalil ; Malrieu, Florent | Springer;Société de Mathématiques Appliquées et Industrielles 2016

Ouvrage

- xiii; 398 p.
ISBN 978-3-662-49767-8

Mathématiques & applications , 0078

Localisation : Collection 1er étage

modélisation # marche aléatoire # processus de Galton-Watson # permutation # partition # mesure de Gibbs # processus de Markov # urne d'Ehrenfest # modèle de Wright-Fisher # généalogie # coalescence # percolation # matrice aléatoire # problème de Dirichlet # processus d'Ornstein-Uhlenbeck # martingale

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