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Documents  62C10 | enregistrements trouvés : 37

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Research School

This tutorial will be a beginner’s introduction to Bayesian statistical modelling and analysis. Simple models and computational tools will be described, followed by a discussion about implementing these approaches in practice. A range of case studies will be presented and possible solutions proposed, followed by an open discussion about other ways that these problems could be tackled.

62C10 ; 62F15 ; 62P12 ; 62P10

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Research schools

This course presents an overview of modern Bayesian strategies for solving imaging inverse problems. We will start by introducing the Bayesian statistical decision theory framework underpinning Bayesian analysis, and then explore efficient numerical methods for performing Bayesian computation in large-scale settings. We will pay special attention to high-dimensional imaging models that are log-concave w.r.t. the unknown image, related to so-called “convex imaging problems”. This will provide an opportunity to establish connections with the convex optimisation and machine learning approaches to imaging, and to discuss some of their relative strengths and drawbacks. Examples of topics covered in the course include: efficient stochastic simulation and optimisation numerical methods that tightly combine proximal convex optimisation with Markov chain Monte Carlo techniques; strategies for estimating unknown model parameters and performing model selection, methods for calculating Bayesian confidence intervals for images and performing uncertainty quantification analyses; and new theory regarding the role of convexity in maximum-a-posteriori and minimum-mean-square-error estimation. The theory, methods, and algorithms are illustrated with a range of mathematical imaging experiments. This course presents an overview of modern Bayesian strategies for solving imaging inverse problems. We will start by introducing the Bayesian statistical decision theory framework underpinning Bayesian analysis, and then explore efficient numerical methods for performing Bayesian computation in large-scale settings. We will pay special attention to high-dimensional imaging models that are log-concave w.r.t. the unknown image, related to ...

49N45 ; 65C40 ; 65C60 ; 65J22 ; 68U10 ; 62C10 ; 62F15 ; 94A08

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Research talks

Data mining methods based on finite mixture models are quite common in many areas of applied science, such as marketing, to segment data and to identify subgroups with specific features. Recent work shows that these methods are also useful in micro econometrics to analyze the behavior of workers in labor markets. Since these data are typically available as time series with discrete states, clustering kernels based on Markov chains with group-specific transition matrices are applied to capture both persistence in the individual time series as well as cross-sectional unobserved heterogeneity. Markov chains clustering has been applied to data from the Austrian labor market, (a) to understanding the effect of labor market entry conditions on long-run career developments for male workers (Frühwirth-Schnatter et al., 2012), (b) to study mothers’ long-run career patterns after first birth (Frühwirth-Schnatter et al., 2016), and (c) to study the effects of a plant closure on future career developments for male worker (Frühwirth-Schnatter et al., 2018). To capture non- stationary effects for the later study, time-inhomogeneous Markov chains based on time-varying group specific transition matrices are introduced as clustering kernels. For all applications, a mixture-of-experts formulation helps to understand which workers are likely to belong to a particular group. Finally, it will be shown that Markov chain clustering is also useful in a business application in marketing and helps to identify loyal consumers within a customer relationship management (CRM) program. Data mining methods based on finite mixture models are quite common in many areas of applied science, such as marketing, to segment data and to identify subgroups with specific features. Recent work shows that these methods are also useful in micro econometrics to analyze the behavior of workers in labor markets. Since these data are typically available as time series with discrete states, clustering kernels based on Markov chains with ...

62C10 ; 62M05 ; 62M10 ; 62H30 ; 62P20 ; 62F15

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Localisation : Colloque 1er étage (MARS)

histoire des mathématiques # histoire des sciences # statistique

62-03 ; 62A15 ; 62Axx ; 62C10 ; 62C12

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- 418 p.
ISBN 978-2-7108-0813-8

Localisation : Colloque 1er étage (MARS)

statistique # méthode bayésienne # probabilité à postériori # Bayes # inférence bayesienne # analyse bayésienne # distribution à priori # test d'hypothèse # estimateur bayésien # propriété asymptotique # série temporelle # BOOTSTRAP

62-06 ; 62C10 ; 62F15

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ISBN 978-90-277-2579-0

Fundamental theories of physics

Localisation : Colloque 1er étage (LARA)

statistique bayesine # tropie

62A15 ; 62C10 ; 62F15 ; 94A17

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- 140 p.
ISBN 978-0-8218-3024-6

Proceedings of the Steklov institute of mathematics , 0124

Localisation : Collection 1er étage

62C10

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ISBN 978-0-19-852356-7

Oxford science publications

Localisation : Colloque 1er étage (ALIC)

ajustement # analyse non stationnaire # approximation # calcul bayessien # chaîne de Markov # climatologie # comparaison # diagramme # donnée auto- régressive # déformation # entropie # estimation paramètrique # facteur bayessien # file d'attente # géométrie # hyperparamètre # image satellitaire # industrie # inférence bayéssienne # lissage # matrice de variance # modèle de prévision # modèle linéaire # modélisation de population # modélisation de rang # modélisation graphique # mélange # méta-analyse # méthode de Monté-Carlo # processus aléatoire # processus de Markov # quadrature bayessienne # robustesse # régression # statistique bayessienne # statistique et estimation non paramètrique # teste # théorie de la décision # théorie des jeux ajustement # analyse non stationnaire # approximation # calcul bayessien # chaîne de Markov # climatologie # comparaison # diagramme # donnée auto- régressive # déformation # entropie # estimation paramètrique # facteur bayessien # file d'attente # géométrie # hyperparamètre # image satellitaire # industrie # inférence bayéssienne # lissage # matrice de variance # modèle de prévision # modèle linéaire # modélisation de population # modélisation ...

62-02 ; 62C10 ; 62C20 ; 62Cxx ; 62Fxx

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ISBN 978-0-444-87746-8

Localisation : Colloque 1er étage (VALE)

approche bayesienne # fond ements de la statis tique # inference bayesienne # probabilite # statistique bayesine

60-06 ; 60Exx ; 62A15 ; 62C10 ; 62Fxx

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- viii; 299 p.
ISBN 978-0-521-51346-3

Cambridge series in statistical and probabilistic mathematics

Localisation : Colloque 1er étage (CAMB)

inférence bayésienne # inférence non-paramétrique # problème bayesien

62F15 ; 62G99 ; 62-06 ; 62C10 ; 00B25

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- 340 p.
ISBN 978-0-8218-2687-4

Contemporary mathematics , 0287

Localisation : Collection 1er étage

statistique # probabilité # méthode algébrique # matrice # théorème central limite # problème bayésien # test d'hypothèse

05B20 ; 60F05 ; 62C10 ; 62H15 ; 62A01

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Research School

The tutorial covers cross-validation, and projection predictive approaches for model assessment, selection and inference after model selection and Bayesian stacking for model averaging. The talk is accompanied with R notebooks using rstanarm, bayesplot, loo, and projpred packages.

62C10 ; 62F15 ; 65C60 ; 62M20

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Research schools

This course presents an overview of modern Bayesian strategies for solving imaging inverse problems. We will start by introducing the Bayesian statistical decision theory framework underpinning Bayesian analysis, and then explore efficient numerical methods for performing Bayesian computation in large-scale settings. We will pay special attention to high-dimensional imaging models that are log-concave w.r.t. the unknown image, related to so-called “convex imaging problems”. This will provide an opportunity to establish connections with the convex optimisation and machine learning approaches to imaging, and to discuss some of their relative strengths and drawbacks. Examples of topics covered in the course include: efficient stochastic simulation and optimisation numerical methods that tightly combine proximal convex optimisation with Markov chain Monte Carlo techniques; strategies for estimating unknown model parameters and performing model selection, methods for calculating Bayesian confidence intervals for images and performing uncertainty quantification analyses; and new theory regarding the role of convexity in maximum-a-posteriori and minimum-mean-square-error estimation. The theory, methods, and algorithms are illustrated with a range of mathematical imaging experiments. This course presents an overview of modern Bayesian strategies for solving imaging inverse problems. We will start by introducing the Bayesian statistical decision theory framework underpinning Bayesian analysis, and then explore efficient numerical methods for performing Bayesian computation in large-scale settings. We will pay special attention to high-dimensional imaging models that are log-concave w.r.t. the unknown image, related to ...

49N45 ; 65C40 ; 65C60 ; 65J22 ; 68U10 ; 62C10 ; 62F15 ; 94A08

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Research schools

This course presents an overview of modern Bayesian strategies for solving imaging inverse problems. We will start by introducing the Bayesian statistical decision theory framework underpinning Bayesian analysis, and then explore efficient numerical methods for performing Bayesian computation in large-scale settings. We will pay special attention to high-dimensional imaging models that are log-concave w.r.t. the unknown image, related to so-called “convex imaging problems”. This will provide an opportunity to establish connections with the convex optimisation and machine learning approaches to imaging, and to discuss some of their relative strengths and drawbacks. Examples of topics covered in the course include: efficient stochastic simulation and optimisation numerical methods that tightly combine proximal convex optimisation with Markov chain Monte Carlo techniques; strategies for estimating unknown model parameters and performing model selection, methods for calculating Bayesian confidence intervals for images and performing uncertainty quantification analyses; and new theory regarding the role of convexity in maximum-a-posteriori and minimum-mean-square-error estimation. The theory, methods, and algorithms are illustrated with a range of mathematical imaging experiments. This course presents an overview of modern Bayesian strategies for solving imaging inverse problems. We will start by introducing the Bayesian statistical decision theory framework underpinning Bayesian analysis, and then explore efficient numerical methods for performing Bayesian computation in large-scale settings. We will pay special attention to high-dimensional imaging models that are log-concave w.r.t. the unknown image, related to ...

49N45 ; 65C40 ; 65C60 ; 65J22 ; 68U10 ; 62C10 ; 62F15 ; 94A08

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Research schools

This course presents an overview of modern Bayesian strategies for solving imaging inverse problems. We will start by introducing the Bayesian statistical decision theory framework underpinning Bayesian analysis, and then explore efficient numerical methods for performing Bayesian computation in large-scale settings. We will pay special attention to high-dimensional imaging models that are log-concave w.r.t. the unknown image, related to so-called “convex imaging problems”. This will provide an opportunity to establish connections with the convex optimisation and machine learning approaches to imaging, and to discuss some of their relative strengths and drawbacks. Examples of topics covered in the course include: efficient stochastic simulation and optimisation numerical methods that tightly combine proximal convex optimisation with Markov chain Monte Carlo techniques; strategies for estimating unknown model parameters and performing model selection, methods for calculating Bayesian confidence intervals for images and performing uncertainty quantification analyses; and new theory regarding the role of convexity in maximum-a-posteriori and minimum-mean-square-error estimation. The theory, methods, and algorithms are illustrated with a range of mathematical imaging experiments. This course presents an overview of modern Bayesian strategies for solving imaging inverse problems. We will start by introducing the Bayesian statistical decision theory framework underpinning Bayesian analysis, and then explore efficient numerical methods for performing Bayesian computation in large-scale settings. We will pay special attention to high-dimensional imaging models that are log-concave w.r.t. the unknown image, related to ...

49N45 ; 65C40 ; 65C60 ; 65J22 ; 68U10 ; 62C10 ; 62F15 ; 94A08

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Research School

This is a short introduction to the many directions of current research in Bayesian computational statistics, from accelerating MCMC algorithms, to using partly deterministic Markov processes like the bouncy particle and the zigzag samplers, to approximating the target or the proposal distributions in such methods. The main illustration focuses on the evaluation of normalising constants and ratios of normalising constants.

62C10 ; 65C60 ; 62F15 ; 65C05

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Research School

This talk focuses on the estimation of the distribution of unobserved nodes in large random graphs from the observation of very few edges. These graphs naturally model tournaments involving a large number of players (the nodes) where the ability to win of each player is unknown. The players are only partially observed through discrete valued scores (edges) describing the results of contests between players. In this very sparse setting, we present the first nonasymptotic risk bounds for maximum likelihood estimators (MLE) of the unknown distribution of the nodes. The proof relies on the construction of a graphical model encoding conditional dependencies that is extremely efficient to study n-regular graphs obtained using a round-robin scheduling. This graphical model allows to prove geometric loss of memory properties and deduce the asymptotic behavior of the likelihood function. Following a classical construction in learning theory, the asymptotic likelihood is used to define a measure of performance for the MLE. Risk bounds for the MLE are finally obtained by subgaussian deviation results derived from concentration inequalities for Markov chains applied to our graphical model. This talk focuses on the estimation of the distribution of unobserved nodes in large random graphs from the observation of very few edges. These graphs naturally model tournaments involving a large number of players (the nodes) where the ability to win of each player is unknown. The players are only partially observed through discrete valued scores (edges) describing the results of contests between players. In this very sparse setting, we ...

62F15 ; 62C10 ; 65C60 ; 65C40

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- 296 p.
ISBN 978-3-540-66455-0

Springer monographs in mathematics

Localisation : Ouvrage RdC (USTU)

analyse stochastique # calcul de Malliavin # classe de Lipschitz # différentiabilité # espace de Sobolev # espace de Wiener # fonctionnelle de Wiener # intégrabilité # intégrale stochastique # mesure # mesure de Wiener # opérateur monotone # probabilité # processus gaussien # singularité et continuité des mesures induites # variable aléatoire

26A16 ; 28C20 ; 46G12 ; 47H05 ; 47H10 ; 60G15 ; 60G30 ; 60G35 ; 60Hxx ; 62C10

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- 609 p.
ISBN 978-0-471-98103-9

Wiley series in probability and mathematical statistics

Localisation : Ouvrage RdC (ZACK)

estimateur # hypothèse statistique # inférence statistique # statistique exhaustive # vraissemblance

62-02 ; 62B05 ; 62C07 ; 62C10 ; 62C15

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- xvii-381 p.
ISBN 978-1-58488-849-9

Texts in statistical science

Localisation : Ouvrage RdC (BUGS)

statistiques # analyse bayesienne # procédures de Bayes # simulation de Monte Carlo

62-01 ; 62C10 ; 62C12

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Z