Institution
Paris Dauphine University
Education•Paris, France•
About: Paris Dauphine University is a education organization based out in Paris, France. It is known for research contribution in the topics: Context (language use) & Population. The organization has 1766 authors who have published 6909 publications receiving 162747 citations. The organization is also known as: Paris Dauphine & Dauphine.
Topics: Context (language use), Population, Approximation algorithm, Bounded function, Nonlinear system
Papers published on a yearly basis
Papers
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TL;DR: In this article, a new method for obtaining quantitative results in stochastic homogenization for linear elliptic equations in divergence form is introduced, which does not use concentration inequalities (such as Poincare or logarithmic Sobolev inequalities in the probability space) and relies instead on a higher (Ck, k ≥ 1) regularity theory for solutions of the heterogeneous equation, which is valid on length scales larger than a specified mesoscopic scale.
Abstract: We introduce a new method for obtaining quantitative results in stochastic homogenization for linear elliptic equations in divergence form. Unlike previous works on the topic, our method does not use concentration inequalities (such as Poincare or logarithmic Sobolev inequalities in the probability space) and relies instead on a higher (Ck, k ≥ 1) regularity theory for solutions of the heterogeneous equation, which is valid on length scales larger than a certain specified mesoscopic scale. This regularity theory, which is of independent interest, allows us to, in effect, localize the dependence of the solutions on the coefficients and thereby accelerate the rate of convergence of the expected energy of the cell problem by a bootstrap argument. The fluctuations of the energy are then tightly controlled using subadditivity. The convergence of the energy gives control of the scaling of the spatial averages of gradients and fluxes (that is, it quantifies the weak convergence of these quantities), which yields, by a new “multiscale” Poincare inequality, quantitative estimates on the sublinearity of the corrector.
60 citations
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TL;DR: In this paper, the authors study the stochastic version of a previous paper of the authors, in which hybrid control for deterministic systems was considered, and show how the dynamic programming approach leads to some involved quasi-variational inequality.
60 citations
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TL;DR: The purpose of this paper has been to trace the development of a way of thinking and type of research which first saw the light of day in France, but which for many years have been influenced and supplemented by work carried out in other European countries.
60 citations
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TL;DR: In this paper, the Bayesian computation with empirical likelihood (BFL) algorithm is used for the analysis of complex stochastic models when the likelihood function is numerically unavailable.
Abstract: Free to read
Approximate Bayesian computation has become an essential tool for the analysis of complex stochastic models when the likelihood function is numerically unavailable. However, the well-established statistical method of empirical likelihood provides another route to such settings that bypasses simulations from the model and the choices of the approximate Bayesian computation parameters (summary statistics, distance, tolerance), while being convergent
in the number of observations. Furthermore, bypassing model simulations may lead to significant time savings in complex models, for instance those found in population genetics. The Bayesian computation with empirical likelihood algorithm we develop in this paper also provides an evaluation of its own performance through an associated effective sample size. The method is illustrated using
several examples, including estimation of standard distributions, time series, and population genetics models.
60 citations
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TL;DR: In this paper, the authors consider the asymptotic behavior of the posterior obtained from approximate Bayesian computation (ABC) and the ensuing posterior mean, and give general results on: (i) the rate of concentration of the ABC posterior on sets containing the true parameter (vector); (ii) the limiting shape of posterior; and (iii) the asyptotic distribution of ABC posterior mean.
Abstract: Approximate Bayesian computation (ABC) is becoming an accepted tool for statistical analysis in models with intractable likelihoods. With the initial focus being primarily on the practical import of ABC, exploration of its formal statistical properties has begun to attract more attention. In this paper we consider the asymptotic behavior of the posterior obtained from ABC and the ensuing posterior mean. We give general results on: (i) the rate of concentration of the ABC posterior on sets containing the true parameter (vector); (ii) the limiting shape of the posterior; and\ (iii) the asymptotic distribution of the ABC posterior mean. These results hold under given rates for the tolerance used within ABC, mild regularity conditions on the summary statistics, and a condition linked to identification of the true parameters. Using simple illustrative examples that have featured in the literature, we demonstrate that the required identification condition is far from guaranteed. The implications of the theoretical results for practitioners of ABC are also highlighted.
60 citations
Authors
Showing all 1819 results
Name | H-index | Papers | Citations |
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Pierre-Louis Lions | 98 | 283 | 57043 |
Laurent D. Cohen | 94 | 417 | 42709 |
Chris Bowler | 87 | 288 | 35399 |
Christian P. Robert | 75 | 535 | 36864 |
Albert Cohen | 71 | 368 | 19874 |
Gabriel Peyré | 65 | 303 | 16403 |
Kerrie Mengersen | 65 | 737 | 20058 |
Nader Masmoudi | 62 | 245 | 10507 |
Roland Glowinski | 61 | 393 | 20599 |
Jean-Michel Morel | 59 | 302 | 29134 |
Nizar Touzi | 57 | 224 | 11018 |
Jérôme Lang | 57 | 277 | 11332 |
William L. Megginson | 55 | 169 | 18087 |
Alain Bensoussan | 55 | 417 | 22704 |
Yves Meyer | 53 | 128 | 14604 |