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36 results on '"Delyon, Bernard"'

1. Stochastic mirror descent for nonparametric adaptive importance sampling

Author

Bianchi, Pascal, Delyon, Bernard, Priser, Victor, and Portier, François

Subjects
Mathematics - Statistics Theory
Abstract

This paper addresses the problem of approximating an unknown probability distribution with density $f$ -- which can only be evaluated up to an unknown scaling factor -- with the help of a sequential algorithm that produces at each iteration $n\geq 1$ an estimated density $q_n$.The proposed method optimizes the Kullback-Leibler divergence using a mirror descent (MD) algorithm directly on the space of density functions, while a stochastic approximation technique helps to manage between algorithm complexity and variability. One of the key innovations of this work is the theoretical guarantee that is provided for an algorithm with a fixed MD learning rate $\eta \in (0,1 )$. The main result is that the sequence $q_n$ converges almost surely to the target density $f$ uniformly on compact sets. Through numerical experiments, we show that fixing the learning rate $\eta \in (0,1 )$ significantly improves the algorithm's performance, particularly in the context of multi-modal target distributions where a small value of $\eta$ allows to increase the chance of finding all modes. Additionally, we propose a particle subsampling method to enhance computational efficiency and compare our method against other approaches through numerical experiments.

Published
2024

3. Safe and adaptive importance sampling: a mixture approach

Author

Delyon, Bernard and Portier, François

Subjects
Mathematics - Statistics Theory, 62G05, 62G07, 65C05
Abstract

This paper investigates adaptive importance sampling algorithms for which the policy, the sequence of distributions used to generate the particles, is a mixture distribution between a flexible kernel density estimate (based on the previous particles), and a "safe" heavy-tailed density. When the share of samples generated according to the safe density goes to zero but not too quickly, two results are established: (i) uniform convergence rates are derived for the policy toward the target density; (ii) a central limit theorem is obtained for the resulting integral estimates. The fact that the asymptotic variance is the same as the variance of an "oracle" procedure with variance-optimal policy, illustrates the benefits of the approach. In addition, a subsampling step (among the particles) can be conducted before constructing the kernel estimate in order to decrease the computational effort without altering the performance of the method. The practical behavior of the algorithms is illustrated in a simulation study., Comment: 35 pages, 4 figures

Published
2019

4. Asymptotic optimality of adaptive importance sampling

Author

Delyon, Bernard and Portier, François

Subjects
Mathematics - Statistics Theory, Statistics - Computation, Statistics - Machine Learning
Abstract

Adaptive importance sampling (AIS) uses past samples to update the \textit{sampling policy} $q_t$ at each stage $t$. Each stage $t$ is formed with two steps : (i) to explore the space with $n_t$ points according to $q_t$ and (ii) to exploit the current amount of information to update the sampling policy. The very fundamental question raised in this paper concerns the behavior of empirical sums based on AIS. Without making any assumption on the allocation policy $n_t$, the theory developed involves no restriction on the split of computational resources between the explore (i) and the exploit (ii) step. It is shown that AIS is asymptotically optimal : the asymptotic behavior of AIS is the same as some "oracle" strategy that knows the targeted sampling policy from the beginning. From a practical perspective, weighted AIS is introduced, a new method that allows to forget poor samples from early stages., Comment: 19 pages, 3 figures

Published
2018

5. On the Asymptotic Normality of Adaptive Multilevel Splitting

Author

Cérou, Frédéric, Delyon, Bernard, Guyader, Arnaud, and Rousset, Mathias

Subjects
Mathematics - Probability
Abstract

Adaptive Multilevel Splitting (AMS for short) is a generic Monte Carlo method for Markov processes that simulates rare events and estimates associated probabilities. Despite its practical efficiency, there are almost no theoretical results on the convergence of this algorithm. The purpose of this paper is to prove both consistency and asymptotic normality results in a general setting. This is done by associating to the original Markov process a level-indexed process, also called a stochastic wave, and by showing that AMS can then be seen as a Fleming-Viot type particle system. This being done, we can finally apply general results on Fleming-Viot particle systems that we have recently obtained., Comment: 38 pages, 5 figures

Published
2018

6. A Central Limit Theorem for Fleming-Viot Particle Systems with Hard Killing

Author

Delyon, Bernard, Cérou, Frédéric, Guyader, Arnaud, and Rousset, Mathias

Subjects
Mathematics - Probability
Abstract

Fleming-Viot type particle systems represent a classical way to approximate the distribution of a Markov process with killing, given that it is still alive at a final deterministic time. In this context, each particle evolves independently according to the law of the underlying Markov process until its killing, and then branches instantaneously on another randomly chosen particle. While the consistency of this algorithm in the large population limit has been recently studied in several articles, our purpose here is to prove Central Limit Theorems under very general assumptions. For this, we only suppose that the particle system does not explode in finite time, and that the jump and killing times have atomless distributions. In particular, this includes the case of elliptic diffusions with hard killing., Comment: 38 pages

Published
2017

7. Mixing properties and central limit theorem for associated point processes

Author

Poinas, Arnaud, Delyon, Bernard, and Lavancier, Frédéric

Subjects
Mathematics - Statistics Theory
Abstract

Positively (resp. negatively) associated point processes are a class of point processes that induce attraction (resp. inhibition) between the points. As an important example, determinantal point processes (DPPs) are negatively associated. We prove $\alpha$-mixing properties for associated spatial point processes by controlling their $\alpha$-coefficients in terms of the first two intensity functions. A central limit theorem for functionals of associated point processes is deduced, using both the association and the $\alpha$-mixing properties. We discuss in detail the case of DPPs, for which we obtain the limiting distribution of sums, over subsets of close enough points of the process, of any bounded function of the DPP. As an application, we get the asymptotic properties of the parametric two-step estimator of some inhomogeneous DPPs.

Published
2017

8. A Central Limit Theorem for Fleming-Viot Particle Systems with Soft Killing

Author

Cerou, Frederic, Delyon, Bernard, Guyader, Arnaud, and Rousset, Mathias

Subjects
Mathematics - Probability
Abstract

The distribution of a Markov process with killing, conditioned to be still alive at a given time, can be approximated by a Fleming-Viot type particle system. In such a system, each particle is simulated independently according to the law of the underlying Markov process, and branches onto another particle at each killing time. The consistency of this method in the large population limit was the subject of several recent articles. In the present paper, we go one step forward and prove a central limit theorem for the law of the Fleming-Viot particle system at a given time under two conditions: a "soft killing" assumption and a boundedness condition involving the "carr\'e du champ" operator of the underlying Markov process.

Published
2016

9. Integral estimation based on Markovian design

Author

Azaïs, Romain, Delyon, Bernard, and Portier, François

Subjects
Mathematics - Statistics Theory, 62G07, G2M05
Abstract

Suppose that a mobile sensor describes a Markovian trajectory in the ambient space. At each time the sensor measures an attribute of interest, e.g., the temperature. Using only the location history of the sensor and the associated measurements, the aim is to estimate the average value of the attribute over the space. In contrast to classical probabilistic integration methods, e.g., Monte Carlo, the proposed approach does not require any knowledge on the distribution of the sensor trajectory. Probabilistic bounds on the convergence rates of the estimator are established. These rates are better than the traditional "root n"-rate, where n is the sample size, attached to other probabilistic integration methods. For finite sample sizes, the good behaviour of the procedure is demonstrated through simulations and an application to the evaluation of the average temperature of oceans is considered., Comment: 45 pages

Published
2016

10. Dependent time changed processes with applications to nonlinear ocean waves

Author

Ailliot, Pierre, Delyon, Bernard, Monbet, Valérie, and Prevosto, Marc

Subjects
Statistics - Methodology
Abstract

Many records in environmental sciences exhibit asymmetric trajectories and there is a need for simple and tractable models which can reproduce such features. In this paper we explore an approach based on applying both a time change and a marginal transformation on Gaussian processes. The main originality of the proposed model is that the time change depends on the observed trajectory. We first show that the proposed model is stationary and ergodic and provide an explicit characterization of the stationary distribution. This result is then used to build both parametric and non-parametric estimates of the time change function whereas the estimation of the marginal transformation is based on up-crossings. Simulation results are provided to assess the quality of the estimates. The model is applied to shallow water wave data and it is shown that the fitted model is able to reproduce important statistics of the data such as its spectrum and marginal distribution which are important quantities for practical applications. An important benefit of the proposed model is its ability to reproduce the observed asymmetries between the crest and the troughs and between the front and the back of the waves by accelerating the chronometer in the crests and in the front of the waves.

Published
2015

11. Investigation of asymmetry in E. coli growth rate

Author

Delyon, Bernard, de Saporta, Benoîte, Krell, Nathalie, and Robert, Lydia

Subjects
Statistics - Applications, Quantitative Biology - Quantitative Methods
Abstract

The data we analyze derives from the observation of numerous cells of the bacterium Escherichia coli (E. coli) growing and dividing. Single cells grow and divide to give birth to two daughter cells, that in turn grow and divide. Thus, a colony of cells from a single ancestor is structured as a binary genealogical tree. At each node the measured data is the growth rate of the bacterium. In this paper, we study two different data sets. One set corresponds to small complete trees, whereas the other one corresponds to long specific sub-trees. Our aim is to compare both sets. This paper is accessible to post graduate students and readers with advanced knowledge in statistics.

Published
2015

13. Concentration inequalities for sums

Author

Bercu, Bernard, Delyon, Bernard, Rio, Emmanuel, Bellomo, Nicola, Series editor, Benzi, Michele, Series editor, Jorgensen, Palle E. T., Series editor, Li, Tatsien, Series editor, Melnik, Roderick, Series editor, Scherzer, Otmar, Series editor, Steinberg, Benjamin, Series editor, Reichel, Lothar, Series editor, Tschinkel, Yuri, Series editor, Yin, G. George, Series editor, Zhang, Ping, Series editor, Bercu, Bernard, Delyon, Bernard, and Rio, Emmanuel

Published
2015
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14. Concentration inequalities for martingales

Author

Bercu, Bernard, Delyon, Bernard, Rio, Emmanuel, Bellomo, Nicola, Series editor, Benzi, Michele, Series editor, Jorgensen, Palle E. T., Series editor, Li, Tatsien, Series editor, Melnik, Roderick, Series editor, Scherzer, Otmar, Series editor, Steinberg, Benjamin, Series editor, Reichel, Lothar, Series editor, Tschinkel, Yuri, Series editor, Yin, G. George, Series editor, Zhang, Ping, Series editor, Bercu, Bernard, Delyon, Bernard, and Rio, Emmanuel

Published
2015
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15. Applications in probability and statistics

Author

Bercu, Bernard, Delyon, Bernard, Rio, Emmanuel, Bellomo, Nicola, Series editor, Benzi, Michele, Series editor, Jorgensen, Palle E. T., Series editor, Li, Tatsien, Series editor, Melnik, Roderick, Series editor, Scherzer, Otmar, Series editor, Steinberg, Benjamin, Series editor, Reichel, Lothar, Series editor, Tschinkel, Yuri, Series editor, Yin, G. George, Series editor, Zhang, Ping, Series editor, Bercu, Bernard, Delyon, Bernard, and Rio, Emmanuel

Published
2015
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16. Classical results

Author

Bercu, Bernard, Delyon, Bernard, Rio, Emmanuel, Bellomo, Nicola, Series editor, Benzi, Michele, Series editor, Jorgensen, Palle E. T., Series editor, Li, Tatsien, Series editor, Melnik, Roderick, Series editor, Scherzer, Otmar, Series editor, Steinberg, Benjamin, Series editor, Reichel, Lothar, Series editor, Tschinkel, Yuri, Series editor, Yin, G. George, Series editor, Zhang, Ping, Series editor, Bercu, Bernard, Delyon, Bernard, and Rio, Emmanuel

Published
2015
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24. On the Optimality of the Kitanidis Filter

Author

Delyon, Bernard, Zhang, Qinghua, Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-Centre National de la Recherche Scientifique (CNRS), Statistical Inference for Structural Health Monitoring (I4S), Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Département Composants et Systèmes (COSYS), and Université Gustave Eiffel-Université Gustave Eiffel

Subjects
unknown input observer, disturbance rejection, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, time varying system, optimal state estimation, Kalman filter
Abstract

As a natural extension of the Kalman filter to systems subject to arbitrary unknown inputs, the Kitanidis filter has been designed by one-step minimization of the trace of the state estimation error covariance matrix. This optimality does not exclude the possibility that, among the class of unbiased recursive filters, another filter may lead to a lower trace criterion. In this paper, it is shown that the Kitanidis filter is indeed optimal in the sense of the whole gain sequence, thus excluding the aforementioned possibility. Moreover, this gain sequence optimality holds also in a stronger sense, in terms of positive definite matrix inequality, which notably implies that the optimality holds not only in the sense of the trace criterion, but also of the matrix spectral norm criterion.

Published
2020

26. Investigation of asymmetry in E. coli growth rate

Author

Delyon, Bernard, de Saporta, Benoîte, Krell, Nathalie, Robert, Lydia, Institut de Recherche Mathématique de Rennes (IRMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Institut Montpelliérain Alexander Grothendieck (IMAG), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Quality control and dynamic reliability (CQFD), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), MICrobiologie de l'ALImentation au Service de la Santé (MICALIS), Institut National de la Recherche Agronomique (INRA)-AgroParisTech, The research of B. de Saporta and N. Krellis partly supported by the ANR, Agence Nationale de la Recherche, grant PIECE 12-JS01-0006-01., ANR-12-JS01-0006,PIECE,Ergodicité, contrôle et statistique pour les PDMP(2012), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-AGROCAMPUS OUEST-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-Centre National de la Recherche Scientifique (CNRS), Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), Institut de Mathématiques et de Modélisation de Montpellier ( I3M ), Université Montpellier 2 - Sciences et Techniques ( UM2 ) -Université de Montpellier ( UM ) -Centre National de la Recherche Scientifique ( CNRS ), Institut Montpelliérain Alexander Grothendieck ( IMAG ), Université de Montpellier ( UM ) -Centre National de la Recherche Scientifique ( CNRS ), Quality control and dynamic reliability ( CQFD ), Institut de Mathématiques de Bordeaux ( IMB ), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux ( UB ) -Institut Polytechnique de Bordeaux ( Bordeaux INP ) -Centre National de la Recherche Scientifique ( CNRS ) -Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux ( UB ) -Institut Polytechnique de Bordeaux ( Bordeaux INP ) -Centre National de la Recherche Scientifique ( CNRS ) -Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National de Recherche en Informatique et en Automatique ( Inria ), MICrobiologie de l'ALImentation au Service de la Santé humaine ( MICALIS ), Institut National de la Recherche Agronomique ( INRA ) -AgroParisTech, ANR-12-JS01-0006,PIECE,Ergodicité, contrôle et statistique pour les PDMP ( 2012 ), Krell, Nathalie, de Saporta, Benoîte, Jeunes Chercheuses et Jeunes Chercheurs - Ergodicité, contrôle et statistique pour les PDMP - - PIECE2012 - ANR-12-JS01-0006 - JC - VALID, and ANR-11-LABX-0020,LEBESGUE,Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation(2011)

Subjects
FOS: Computer and information sciences, [ STAT ] Statistics [stat], Tests, Dependent data, Binary tree, Statistics - Applications, Quantitative Biology - Quantitative Methods, [STAT] Statistics [stat], [STAT]Statistics [stat], Linear regression models, Branching processes, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], FOS: Biological sciences, Autoregressive models, Applications (stat.AP), [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], Quantitative Methods (q-bio.QM), ComputingMilieux_MISCELLANEOUS
Abstract

The data we analyze derives from the observation of numerous cells of the bacterium Escherichia coli (E. coli) growing and dividing. Single cells grow and divide to give birth to two daughter cells, that in turn grow and divide. Thus, a colony of cells from a single ancestor is structured as a binary genealogical tree. At each node the measured data is the growth rate of the bacterium. In this paper, we study two different data sets. One set corresponds to small complete trees, whereas the other one corresponds to long specific sub-trees. Our aim is to compare both sets. This paper is accessible to post graduate students and readers with advanced knowledge in statistics.

Published
2019

30. A Central Limit Theorem for Fleming-Viot Particle Systems with Hard Killing

Author

Cérou, Frédéric, Delyon, Bernard, Guyader, Arnaud, Rousset, Mathias, Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), SIMulation pARTiculaire de Modèles Stochastiques (SIMSMART), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Pierre et Marie Curie - Paris 6 - UFR de Médecine Pierre et Marie Curie (UPMC), Université Pierre et Marie Curie - Paris 6 (UPMC), IRMAR-STAT, ANR-14-CE23-0012,COSMOS,Statistique numérique et simulation moléculaire(2014), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-AGROCAMPUS OUEST, Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA)-Inria Rennes – Bretagne Atlantique, Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), Applications of interacting particle systems to statistics ( ASPI ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Centre National de la Recherche Scientifique ( CNRS ), Université Pierre et Marie Curie - Paris 6 - UFR de Médecine Pierre et Marie Curie ( UPMC ), Université Pierre et Marie Curie - Paris 6 ( UPMC ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ) -Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ) -Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique ( Inria ), ANR-14-CE23-0012,COSMOS,Statistique numérique et simulation moléculaire ( 2014 ), Guillemer, Marie-Annick, and Appel à projets générique - Statistique numérique et simulation moléculaire - - COSMOS2014 - ANR-14-CE23-0012 - Appel à projets générique - VALID

Subjects
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR], [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], Interacting particle systems, Probability (math.PR), process with killing, FOS: Mathematics, sequential MonteCarlo, [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR], Mathematics - Probability, 82C22, 82C80, 65C05, 60J25, 60K35, 60K37
Abstract

Fleming-Viot type particle systems represent a classical way to approximate the distribution of a Markov process with killing, given that it is still alive at a final deterministic time. In this context, each particle evolves independently according to the law of the underlying Markov process until its killing, and then branches instantaneously on another randomly chosen particle. While the consistency of this algorithm in the large population limit has been recently studied in several articles, our purpose here is to prove Central Limit Theorems under very general assumptions. For this, we only suppose that the particle system does not explode in finite time, and that the jump and killing times have atomless distributions. In particular, this includes the case of elliptic diffusions with hard killing., 38 pages

Published
2017

31. Exponential inequalities for dependent processes

Author

Delyon, Bernard, Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), Delyon, Bernard, Institut de Recherche Mathématique de Rennes (IRMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, and Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)

Subjects
[MATH.MATH-PR] Mathematics [math]/Probability [math.PR], [STAT.TH] Statistics [stat]/Statistics Theory [stat.TH], [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], [ STAT.TH ] Statistics [stat]/Statistics Theory [stat.TH], weak dependence, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Mixing, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], random fields, exponential inequality, [ MATH.MATH-ST ] Mathematics [math]/Statistics [math.ST], [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], 60F99, [ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR]
Abstract

We give exponential inequalities and Gaussian approximation results for sums of weakly dependent variables. These results lead to generalizations of Bernstein and Hoeffding inequalities, where an extra control term is added; this term contains conditional moments of the variables.

Published
2015

32. Dependent time changed processes with applications to nonlinear ocean waves

Author

Ailliot , Pierre, Delyon , Bernard, Monbet , Valérie, Prevosto , Marc, Laboratoire de Mathématiques de Bretagne Atlantique ( LMBA ), Université de Brest ( UBO ) -Université de Bretagne Sud ( UBS ) -Centre National de la Recherche Scientifique ( CNRS ), Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), Applications of interacting particle systems to statistics ( ASPI ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ) -Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ) -Inria Rennes – Bretagne Atlantique, Institut National de Recherche en Informatique et en Automatique ( Inria ), Institut Français de Recherche pour l'Exploitation de la Mer - Brest ( IFREMER ), and Institut Français de Recherche pour l'Exploitation de la Mer ( IFREMER )

Subjects
Methodology (stat.ME), FOS: Computer and information sciences, ocean waves, time change, Gaussian processes, nonlinear processes, [ MATH.MATH-ST ] Mathematics [math]/Statistics [math.ST], Statistics - Methodology
Abstract

Many records in environmental sciences exhibit asymmetric trajectories and there is a need for simple and tractable models which can reproduce such features. In this paper we explore an approach based on applying both a time change and a marginal transformation on Gaussian processes. The main originality of the proposed model is that the time change depends on the observed trajectory. We first show that the proposed model is stationary and ergodic and provide an explicit characterization of the stationary distribution. This result is then used to build both parametric and non-parametric estimates of the time change function whereas the estimation of the marginal transformation is based on up-crossings. Simulation results are provided to assess the quality of the estimates. The model is applied to shallow water wave data and it is shown that the fitted model is able to reproduce important statistics of the data such as its spectrum and marginal distribution which are important quantities for practical applications. An important benefit of the proposed model is its ability to reproduce the observed asymmetries between the crest and the troughs and between the front and the back of the waves by accelerating the chronometer in the crests and in the front of the waves.

Published
2015

34. Concentration Inequalities for Sums and Martingales / by Bernard Bercu, Bernard Delyon, Emmanuel Rio.

Author

Bercu, Bernard. author., Delyon, Bernard. author., Rio, Emmanuel. author., SpringerLink (Online service), Bercu, Bernard. author., Delyon, Bernard. author., Rio, Emmanuel. author., and SpringerLink (Online service)

Abstract

The purpose of this book is to provide an overview of historical and recent results on concentration inequalities for sums of independent random variables and for martingales. The first chapter is devoted to classical asymptotic results in probability such as the strong law of large numbers and the central limit theorem. Our goal is to show that it is really interesting to make use of concentration inequalities for sums and martingales. The second chapter deals with classical concentration inequalities for sums of independent random variables such as the famous Hoeffding, Bennett, Bernstein and Talagrand inequalities. Further results and improvements are also provided such as the missing factors in those inequalities. The third chapter concerns concentration inequalities for martingales such as Azuma-Hoeffding, Freedman and De la Pena inequalities. Several extensions are also provided. The fourth chapter is devoted to applications of concentration inequalities in probability and statistics.

Published
2015

35. Investigation of asymmetry in E. coli growth rate.

Author

Delyon, Bernard, de Saporta, Benoîte, Krell, Nathalie, and Robert, Lydia

Subjects
*SYMMETRY (Biology), *ESCHERICHIA coli growth, *BRANCHING processes
Abstract

The data we analyze derives from the observation of numerous cells of the bacterium Escherichia coli (E. coli) growing and dividing. Single cells grow and divide to give birth to two daughter cells, that in turn grow and divide. Thus, a colony of cells from a single ancestor is structured as a binary genealogical tree. At each node the measured data is the growth rate of the bacterium. In this paper, we study two different data sets. One set corresponds to small complete trees, whereas the other one corresponds to long specific sub-trees. Our aim is to compare both sets. This paper is accessible to post graduate students and readers with advanced knowledge in statistics. [ABSTRACT FROM AUTHOR]

Published
2018

36. FrontMatter.

Author

Bercu, Bernard, Delyon, Bernard, and Rio, Emmanuel

Published
2015

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