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12 results on '"Department of Statistics [Vancouver] (UBC Statistics)"'

1. A review of species role concepts in food webs

Author

Giulio Valentino Dalla Riva, Marília P. Gaiarsa, E. Fernando Cagua, Alyssa R. Cirtwill, Camille Coux, Malyon D. Bimler, D. Matthias Dehling, Linköping University (LIU), Department of Statistics [Vancouver] (UBC Statistics), University of British Columbia (UBC), University of Canterbury [Christchurch], Universidade de São Paulo (USP), Department of Entomology [Riverside], University of California [Riverside] (UCR), University of California-University of California, School of Biological Sciences, University of Queensland [Brisbane], Santé et agroécologie du vignoble (UMR SAVE), and Institut National de la Recherche Agronomique (INRA)-Université de Bordeaux (UB)-Institut des Sciences de la Vigne et du Vin (ISVV)-Ecole Nationale Supérieure des Sciences Agronomiques de Bordeaux-Aquitaine (Bordeaux Sciences Agro)

Subjects
0106 biological sciences, Ecological niche, Ekologi, eltonian niche, Ecology, 010604 marine biology & hydrobiology, media_common.quotation_subject, [SDV]Life Sciences [q-bio], Eltonian niche, network structure, Ambiguity, 010603 evolutionary biology, 01 natural sciences, Epistemology, Role Concepts, [SDE]Environmental Sciences, Sociology, Centrality, Ecology, Evolution, Behavior and Systematics, media_common
Abstract

Many different concepts have been used to describe species' roles in food webs (i.e., the ways in which species participate in their communities as consumers and resources). As each concept focuses on a different aspect of food-web structure, it can be difficult to relate these concepts to each other and to other aspects of ecology. Here we use the Eltonian niche as an overarching framework, within which we summarize several commonly-used role concepts (degree, trophic level, motif roles, and centrality). We focus mainly on the topological versions of these concepts but, where dynamical versions of a role concept exist, we acknowledge these as well. Our aim is to highlight areas of overlap and ambiguity between different role concepts and to describe how these roles can be used to group species according to different strategies (i.e., equivalence and functional roles). The existence of “gray areas” between role concepts make it essential for authors to carefully consider both which role concept(s) are most appropriate for the analyses they wish to conduct and what aspect of species' niches (if any) they wish to address. The ecological meaning of differences between species' roles can change dramatically depending on which role concept(s) are used.

Published
2018
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2. Bayesian Feature Weighting for Unsupervised Learning‚ with Application to Object Recognition

Author

Peter Carbonetto, Nando de Freitas, Paul Gustafson, Natalie Thompson, Computer Science Department (UBC-Computer Science), University of British Columbia (UBC), Department of Statistics [Vancouver] (UBC Statistics), Microsoft, Christopher M. Bishop and Brendan J. Frey, and Team, THOTH

Subjects
ComputingMethodologies_PATTERNRECOGNITION, [INFO.INFO-CV] Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV], LEAR, [INFO.INFO-CV]Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV]
Abstract

International audience; We present a method for variable selection/weighting in an unsupervised learning context using Bayesian shrinkage. The basis for the model parameters and cluster assignments can be computed simultaneous using an efficient EM algorithm. Applying our Bayesian shrinkage model to a complex problem in object recognition (Duygulu, Barnard, de Freitas and Forsyth 2002), our experiments yied good results.

Published
2016

3. Bayesian Inference for Linear Dynamic Models With Dirichlet Process Mixtures

Author

Philippe Vanheeghe, Manuel Davy, François Caron, Arnaud Doucet, Emmanuel Duflos, Sequential Learning (SEQUEL), Laboratoire d'Informatique Fondamentale de Lille (LIFL), Université de Lille, Sciences et Technologies-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lille, Sciences Humaines et Sociales-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lille, Sciences Humaines et Sociales-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire d'Automatique, Génie Informatique et Signal (LAGIS), Université de Lille, Sciences et Technologies-Centrale Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Centre National de la Recherche Scientifique (CNRS), LAGIS-SI, Laboratoire d'Automatique, Génie Informatique et Signal (LAGIS), Université de Lille, Sciences et Technologies-Centrale Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Centrale Lille-Centre National de la Recherche Scientifique (CNRS), Department of Statistics [Vancouver] (UBC Statistics), University of British Columbia (UBC), Université de Lille, Sciences et Technologies-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lille, Sciences Humaines et Sociales-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lille, Sciences Humaines et Sociales-Centre National de la Recherche Scientifique (CNRS)-Laboratoire d'Automatique, Génie Informatique et Signal (LAGIS), Université de Lille, Sciences et Technologies-Centrale Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, and Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
Mathematical optimization, Monte Carlo method, Mathematics - Statistics Theory, Statistics Theory (math.ST), 02 engineering and technology, Bayesian inference, 01 natural sciences, Bayesian nonparametrics, 010104 statistics & probability, symbols.namesake, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], FOS: Mathematics, Markov chain Monte Carlo (MCMC), 0202 electrical engineering, electronic engineering, information engineering, 0101 mathematics, Electrical and Electronic Engineering, Rao-Blackwellization, Mathematics, particle filter, Sequential estimation, 020206 networking & telecommunications, Markov chain Monte Carlo, Dirichlet process mixture (DPM), [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], Kalman filter, Dirichlet process, Gaussian noise, Signal Processing, symbols, Particle filter, Algorithm
Abstract

International audience; Using Kalman techniques, it is possible to perform optimal estimation in linear Gaussian state-space models. We address here the case where the noise probability density functions are of unknown functional form. A flexible Bayesian nonparametric noise model based on Dirichlet process mixtures is introduced. Efficient Markov chain Monte Carlo and Sequential Monte Carlo methods are then developed to perform optimal batch and sequential estimation in such contexts. The algorithms are applied to blind deconvolution and change point detection. Experimental results on synthetic and real data demonstrate the efficiency of this approach in various contexts.

Published
2008
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4. Sparsity-Promoting Bayesian Dynamic Linear Models

Author

Caron, François, Bornn, Luke, Doucet, Arnaud, Advanced Learning Evolutionary Algorithms (ALEA), Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS), 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), Department of Statistics [Vancouver] (UBC Statistics), University of British Columbia (UBC), Department of Statistics [Oxford], University of Oxford [Oxford], INRIA, 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), and University of Oxford

Subjects
[STAT.ML]Statistics [stat]/Machine Learning [stat.ML], dynamic regression, sparsity, particle filters, Gaussian mixture models, particle MCMC, [STAT.CO]Statistics [stat]/Computation [stat.CO], generalized hyperbolic, [STAT.ME]Statistics [stat]/Methodology [stat.ME]
Abstract

Sparsity-promoting priors have become increasingly popular over recent years due to an increased number of regression and classification applications involving a large number of predictors. In time series applications where observations are collected over time, it is often unrealistic to assume that the underlying sparsity pattern is fixed. We propose here an original class of flexible Bayesian linear models for dynamic sparsity modelling. The proposed class of models expands upon the existing Bayesian literature on sparse regression using generalized multivariate hyperbolic distributions. The properties of the models are explored through both analytic results and simulation studies. We demonstrate the model on a financial application where it is shown that it accurately represents the patterns seen in the analysis of stock and derivative data, and is able to detect major events by filtering an artificial portfolio of assets.

Published
2012

5. Fluctuations of Interacting Markov Chain Monte Carlo Models

Author

Bercu, Bernard, Del Moral, Pierre, Doucet, Arnaud, 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), Quality control and dynamic reliability (CQFD), 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), Advanced Learning Evolutionary Algorithms (ALEA), Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS), Dept of Statistics & Dept of Computer Science, University of British Columbia (UBC), Department of Statistics [Vancouver] (UBC Statistics), 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), and 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

Subjects
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 47H20, 60G35, 60J85, 62G09, 47D08, 47G10, 62L20
Abstract

International audience; We present a functional central limit theorem for a general class of interacting Markov chain Monte Carlo interpretations of discrete generation measure-valued equations. The path space models associated with these stochastic processes belong to the class of nonlinear Markov chains interacting with their empirical occupation measures. We develop an original theoretical analysis based on resolvent operators and semigroup techniques to analyze the fluctuation of their occupation measures around their limiting value. We also present a set of simple regularity conditions that applies to interacting Markov chain Monte Carlo models on path spaces, yielding what seems to be the first fluctuation theorems for this class of self-interacting models.

Published
2012

6. On Adaptive Resampling Procedures for Sequential Monte Carlo Methods

Author

Del Moral, Pierre, Doucet, Arnaud, Jasra, Ajay, Institut de Mathématiques de Bordeaux (IMB), 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), Advanced Learning Evolutionary Algorithms (ALEA), Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS), Dept of Statistics & Dept of Computer Science, University of British Columbia (UBC), Department of Statistics [Vancouver] (UBC Statistics), Department of Computing [London], Biomedical Image Analysis Group [London] (BioMedIA), Imperial College London-Imperial College London, and 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)

Subjects
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 65C05, 60G35, 60J85, 62G09, 47D08, 47G10, 62L20
Abstract

International audience; Sequential Monte Carlo (SMC) methods are a general class of techniques to sample approximately from any sequence of probability distributions. These distributions are approximated by a cloud of weighted samples which are propagated over time using a combination of importance sampling and resampling steps. This article is concerned with the convergence analysis of a class of SMC methods where the times at which resampling occurs are computed on-line using criteria such as the effective sample size. This is a popular approach amongst practitioners but there are very few convergence results available for these methods. It is shown here that these SMC algorithms correspond to a particle approximation of a Feynman-Kac flow of measures on adaptive excursion spaces. By combining a non-linear distribution flow analysis to an original coupling technique, we obtain functional central limit theorems and uniform exponential concentration estimates for these algorithms. The original exponential concentration theorems presented in this study significantly improve previous concentration estimates obtained for SMC algorithms.

Published
2012
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7. An Adaptive Interacting Wang-Landau Algorithm for Automatic Density Exploration

Author

Luke Bornn, Pierre Del Moral, Arnaud Doucet, Pierre Jacob, Department of Statistics [Vancouver] (UBC Statistics), University of British Columbia (UBC), Centre de Recherche en Économie et Statistique (CREST), Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] (ENSAI)-École polytechnique (X)-École Nationale de la Statistique et de l'Administration Économique (ENSAE Paris)-Centre National de la Recherche Scientifique (CNRS), CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Advanced Learning Evolutionary Algorithms (ALEA), Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS), Dept of Statistics & Dept of Computer Science, 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), Department of Statistics, Department of Statistics [Oxford], University of Oxford [Oxford]-University of Oxford [Oxford], Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-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), and University of Oxford-University of Oxford

Subjects
Statistics and Probability, FOS: Computer and information sciences, Computer science, 01 natural sciences, Statistics - Computation, Statistics - Applications, Hybrid Monte Carlo, Methodology (stat.ME), 010104 statistics & probability, symbols.namesake, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], 0103 physical sciences, Discrete Mathematics and Combinatorics, Applications (stat.AP), 0101 mathematics, 010306 general physics, [STAT.CO]Statistics [stat]/Computation [stat.CO], Monte Carlo algorithm, Statistics - Methodology, Computation (stat.CO), [STAT.AP]Statistics [stat]/Applications [stat.AP], Rejection sampling, Markov chain Monte Carlo, [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], symbols, Monte Carlo integration, Monte Carlo method in statistical physics, Parallel tempering, Statistics, Probability and Uncertainty, Particle filter, Algorithm, [STAT.ME]Statistics [stat]/Methodology [stat.ME]
Abstract

While statisticians are well-accustomed to performing exploratory analysis in the modeling stage of an analysis, the notion of conducting preliminary general-purpose exploratory analysis in the Monte Carlo stage (or more generally, the model-fitting stage) of an analysis is an area which we feel deserves much further attention. Towards this aim, this paper proposes a general-purpose algorithm for automatic density exploration. The proposed exploration algorithm combines and expands upon components from various adaptive Markov chain Monte Carlo methods, with the Wang-Landau algorithm at its heart. Additionally, the algorithm is run on interacting parallel chains -- a feature which both decreases computational cost as well as stabilizes the algorithm, improving its ability to explore the density. Performance is studied in several applications. Through a Bayesian variable selection example, the authors demonstrate the convergence gains obtained with interacting chains. The ability of the algorithm's adaptive proposal to induce mode-jumping is illustrated through a trimodal density and a Bayesian mixture modeling application. Lastly, through a 2D Ising model, the authors demonstrate the ability of the algorithm to overcome the high correlations encountered in spatial models., Comment: 33 pages, 20 figures (the supplementary materials are included as appendices)

Published
2011
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8. Combining Mixture Components for Clustering

Author

Raphael Gottardo, Jean Patrick Baudry, Gilles Celeux, Kenneth Lo, Adrian E. Raftery, Laboratoire de Mathématiques d'Orsay (LM-Orsay), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Department of Statistics, University of Washington [Seattle], Model selection in statistical learning (SELECT), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Department of Statistics [Vancouver] (UBC Statistics), University of British Columbia (UBC), Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
Statistics and Probability, Fuzzy clustering, Computer science, Gaussian, Correlation clustering, Single-linkage clustering, multivariate normal distribution, computer.software_genre, 01 natural sciences, Complete-linkage clustering, Article, 010104 statistics & probability, 03 medical and health sciences, symbols.namesake, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], BIC, Discrete Mathematics and Combinatorics, Statistical physics, 0101 mathematics, Cluster analysis, 030304 developmental biology, 0303 health sciences, mixture model, flow cytometry, model-based clustering, [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], Mixture model, Determining the number of clusters in a data set, symbols, Data mining, Statistics, Probability and Uncertainty, entropy, computer
Abstract

Model-based clustering consists of fitting a mixture model to data and identifying each cluster with one of its components. Multivariate normal distributions are typically used. The number of clusters is usually determined from the data, often using BIC. In practice, however, individual clusters can be poorly fitted by Gaussian distributions, and in that case model-based clustering tends to represent one non-Gaussian cluster by a mixture of two or more Gaussian distributions. If the number of mixture components is interpreted as the number of clusters, this can lead to overestimation of the number of clusters. This is because BIC selects the number of mixture components needed to provide a good approximation to the density, rather than the number of clusters as such. We propose first selecting the total number of Gaussian mixture components, K, using BIC and then combining them hierarchically according to an entropy criterion. This yields a unique soft clustering for each number of clusters less than or equal to K. These clusterings can be compared on substantive grounds, and we also describe an automatic way of selecting the number of clusters via a piecewise linear regression fit to the rescaled entropy plot. We illustrate the method with simulated data and a flow cytometry dataset. Supplemental Materials are available on the journal Web site and described at the end of the paper.

Published
2010

9. Bayesian clustering in decomposable graphs

Author

Luke Bornn, François Caron, Department of Statistics [Vancouver] (UBC Statistics), University of British Columbia (UBC), Advanced Learning Evolutionary Algorithms (ALEA), Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS), 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), and 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)

Subjects
Statistics and Probability, FOS: Computer and information sciences, Decomposable graphs, media_common.quotation_subject, Bayesian probability, Bayesian analysis, Machine Learning (stat.ML), [STAT.OT]Statistics [stat]/Other Statistics [stat.ML], Machine learning, computer.software_genre, 01 natural sciences, Statistics - Applications, Clustering, Methodology (stat.ME), 010104 statistics & probability, Statistics - Machine Learning, Voting, 0502 economics and business, Prior probability, Applications (stat.AP), Graphical model, 0101 mathematics, Cluster analysis, Statistics - Methodology, 050205 econometrics, media_common, Mathematics, [STAT.AP]Statistics [stat]/Applications [stat.AP], Product partition models, business.industry, American voting, Applied Mathematics, 05 social sciences, Agriculture, Partition (database), Graph, Bayesian clustering, Artificial intelligence, business, computer, [STAT.ME]Statistics [stat]/Methodology [stat.ME]
Abstract

In this paper we propose a class of prior distributions on decomposable graphs, allowing for improved modeling flexibility. While existing methods solely penalize the number of edges, the proposed work empowers practitioners to control clustering, level of separation, and other features of the graph. Emphasis is placed on a particular prior distribution which derives its motivation from the class of product partition models; the properties of this prior relative to existing priors is examined through theory and simulation. We then demonstrate the use of graphical models in the field of agriculture, showing how the proposed prior distribution alleviates the inflexibility of previous approaches in properly modeling the interactions between the yield of different crop varieties., 3 figures, 1 table

Published
2010
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10. Interacting Markov chain Monte Carlo methods for solving nonlinear measure-valued equations

Author

Pierre Del Moral, Arnaud Doucet, Institut de Mathématiques de Bordeaux (IMB), 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), Advanced Learning Evolutionary Algorithms (ALEA), Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS), Department of Statistics [Vancouver] (UBC Statistics), University of British Columbia (UBC), Dept of Statistics & Dept of Computer Science, and 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)

Subjects
Statistics and Probability, Uniform convergence, Feynman–Kac formulae, Markov chain Monte Carlo methods, Metropolis-Hastings algorithm, sequential Monte Carlo, 01 natural sciences, Measure (mathematics), 010104 statistics & probability, symbols.namesake, 62G09, Metropolis–Hastings algorithm, FOS: Mathematics, Applied mathematics, 60J85, 62L20, 0101 mathematics, self-interacting processes, 47H20, Mathematics, Probability measure, Sequence, Markov chain, 47D08, Stochastic process, Probability (math.PR), 010102 general mathematics, 60G35, 47G10, Markov chain Monte Carlo, 16. Peace & justice, Feynman-Kac formulae, time-inhomogeneous Markov chains, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Nonlinear system, symbols, sequential Monte Carlo methods, Statistics, Probability and Uncertainty, Mathematics - Probability
Abstract

We present a new class of interacting Markov chain Monte Carlo algorithms for solving numerically discrete-time measure-valued equations. The associated stochastic processes belong to the class of self-interacting Markov chains. In contrast to traditional Markov chains, their time evolutions depend on the occupation measure of their past values. This general methodology allows us to provide a natural way to sample from a sequence of target probability measures of increasing complexity. We develop an original theoretical analysis to analyze the behavior of these iterative algorithms which relies on measure-valued processes and semigroup techniques. We establish a variety of convergence results including exponential estimates and a uniform convergence theorem with respect to the number of target distributions. We also illustrate these algorithms in the context of Feynman-Kac distribution flows., Comment: Published in at http://dx.doi.org/10.1214/09-AAP628 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

Published
2010
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11. Discussions on 'Riemann manifold Langevin and Hamiltonian Monte Carlo methods'

Author

Barthelme, Simon, Beffy, Magali, Chopin, Nicolas, Doucet, Arnaud, Jacob, Pierre, Johansen, Adam M., Marin, Jean-Michel, Robert, Christian P., Technische Universität Berlin (TU), Centre de Recherche en Économie et Statistique (CREST), Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] (ENSAI)-École polytechnique (X)-École Nationale de la Statistique et de l'Administration Économique (ENSAE Paris)-Centre National de la Recherche Scientifique (CNRS), Dept of Statistics & Dept of Computer Science, UBC, University of British Columbia (UBC), CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Department of Statistics [Vancouver] (UBC Statistics), Institut de Mathématiques et de Modélisation de Montpellier (I3M), Centre National de la Recherche Scientifique (CNRS)-Université Montpellier 2 - Sciences et Techniques (UM2)-Université de Montpellier (UM), Institut Universitaire de France (IUF), Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.), and Robert, Christian

Subjects
FOS: Computer and information sciences, [STAT.CO]Statistics [stat]/Computation [stat.CO], Statistics - Computation, [STAT.CO] Statistics [stat]/Computation [stat.CO], Mathematics::Symplectic Geometry, Computation (stat.CO), Statistics::Computation
Abstract

This is a collection of discussions of `Riemann manifold Langevin and Hamiltonian Monte Carlo methods" by Girolami and Calderhead, to appear in the Journal of the Royal Statistical Society, Series B., Comment: 6 pages, one figure

Published
2010
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12. A Functional Central Limit Theorem for a Class of Interacting Markov Chain Monte Carlo Models

Author

Bercu, Bernard, Del Moral, Pierre, Doucet, Arnaud, Institut de Mathématiques de Bordeaux (IMB), 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), Quality control and dynamic reliability (CQFD), 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, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Advanced Learning Evolutionary Algorithms (ALEA), Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS), Dept of Statistics & Dept of Computer Science, University of British Columbia (UBC), Department of Statistics [Vancouver] (UBC Statistics), 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), and 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

Subjects
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR], martingale limit theorems, random fields, Markov chain Monte Carlo models, 47H20, 60G35, 60J85, 62G09, 47D08, 47G10, 62L20, Multivariate and functional central limit theorems, and Feynman-Kac integrals, self-interacting Markov chains
Abstract

International audience; We present a functional central limit theorem for a new class of interaction Markov chain Monte Carlo interpretations of discrete generation measure valued equations. We provide an original stochastic analysis based on semigroup techniques on distribution spaces and fluctuation theorems for self-interaction random fields. Besides the fluctuation analysis of these models, we also present a series of sharp $\LL_m$-mean error bounds in terms of the semigroup associated with the first order expansion of the limiting measure valued process, yielding what seems to be the first results of this type for this class of interacting processes. We illustrate these results in the context of Feynman-Kac integration semigroups arising in physics, biology and stochastic engineering science.

Published
2009

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