Institut de Mathématiques de Marseille, UMR 7373




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29 octobre 2018: 2 événements

Séminaire

  • Séminaire Statistique

    Lundi 29 octobre 11:00-12:00 - Kerrie MENGERSEN - Queensland University of Technology

    Non-informative and weakly informative Bayesian priors

    Résumé : Priors play a key role in Bayesian modelling, computation and inference. There is interest in the formulation of so-called uninformative or weakly informative priors, which carry little to no information in the posterior distribution, given the data. Although there has been a substantial amount of research on these types of priors, the increasing complexity of models and the expansion of computational algorithms motivates new ideas and insights. In this presentation, I will discuss some recent research into the formulation of such priors for mixture models, hypothesis testing and model evaluation. The integral role of approximate Bayesian computation (ABC) as a computational tool will also be highlighted. This work is joint with a number of co-authors, listed below.
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    References :
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    Z van Havre, N White, J Rousseau, K Mengersen (2015) Overfitting Bayesian Mixture Models with an Unknown Number of Components. PLoS One. 10, 1-27.
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    K Kanary, K Mengersen, CP Robert, J Rousseau (2018) Testing hypotheses via a mixture estimation model. arXiv:1412.2044.
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    DJ Nott, CC Drovandi, K Mengersen, M Evans (2018) Approximation of Bayesian predictive p-values with regression ABC. Bayesian Analysis. 13, 59-83.
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    J Rousseau, K Mengersen (2011) Asymptotic behaviour of the posterior distribution in overfitted mixture models. JRSS Series B. 73, 689–710
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    W Xueou, DJ Nott, CC Drovandi, K Mengersen, M Evans (2018) Using history matching for prior choice. Technometrics. To appear.

    JPEG - 21.3 ko
    Kerrie MENGERSEN

    Lieu : FRUMAM 2e étage - Aix-Marseille Université - Site St Charles
    3, place Victor Hugo - case 39
    13331 MARSEILLE Cedex 03

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  • Séminaire Statistique

    Lundi 29 octobre 14:00-15:00 - Rainer VON SACHS - Université Catholique de Louvain

    Intrinsic wavelet smoothing of curves and surfaces of Hermitian positive definite matrices

    Résumé : In multivariate time series analysis, non-degenerate autocovariance and spectral density matrices are necessarily Hermitian and positive definite and it is important to preserve these properties in any estimation procedure. Our main contribution is the development of intrinsic wavelet transforms and nonparametric wavelet regression for curves in the non-Euclidean space of Hermitian positive definite matrices. The primary focus is on the construction of intrinsic average-interpolation wavelet transforms in the space equipped with a natural invariant Riemannian metric. In addition, we derive the wavelet coefficient decay and linear wavelet thresholding convergence rates of intrinsically smooth curves of Hermitian positive definite matrices. The intrinsic wavelet transforms are computationally fast and nonlinear wavelet shrinkage or thresholding captures localized features, such as cups or kinks, in the matrix-valued curves. In the context of nonparametric spectral estimation, the intrinsic linear or nonlinear wavelet spectral estimator satisfies the important property that it is equivariant under a change of basis of the time series, in contrast to most existing approaches. The finite-sample performance of the intrinsic wavelet spectral estimator based on nonlinear tree-structured trace thresholding is benchmarked against several state-of-the-art nonparametric curve regression procedures in the Riemannian manifold by means of simulated time series data.
    This is joint work with Joris Chau (Université catholique de Louvain).

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    Rainer VON SACHS

    Lieu : FRUMAM 2e étage - Aix-Marseille Université - Site St Charles
    3, place Victor Hugo - case 39
    13331 MARSEILLE Cedex 03

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29 octobre 2018: 1 événement

groupe de travail

  • Agenda ERC IChaos

    Du 19 octobre au 1er novembre - Alexander BUFETOV, Alexey KLIMENKO & Sergey BEREZIN

    Small Group of Work

    Lieu : IGESA Center - Porquerolles

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