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Documents  Chopin, Nicolas | enregistrements trouvés : 5

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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 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 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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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 ...

62F15 ; 62D05 ; 65C05 ; 60J22 ; 62M05 ; 62M20

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