The Experts below are selected from a list of 6933 Experts worldwide ranked by ideXlab platform
Ajay Jasra - One of the best experts on this subject based on the ideXlab platform.
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Multilevel Particle Filters: Normalizing Constant Estimation
Statistics and Computing, 2016Co-Authors: Ajay Jasra, Kengo Kamatani, Peprah Osei, Yan ZhouAbstract:In this article, we introduce two new estimates of the Normalizing Constant (or marginal likelihood) for partially observed diffusion (POD) processes, with discrete observations. One estimate is biased but non-negative and the other is unbiased but not almost surely non-negative. Our method uses the multilevel particle filter of Jasra et al. (Multilevel particle lter, arXiv:1510.04977 , 2015). We show that, under assumptions, for Euler discretized PODs and a given $$\varepsilon >0$$ in order to obtain a mean square error (MSE) of $${\mathcal {O}}(\varepsilon ^2)$$ one requires a work of $${\mathcal {O}}(\varepsilon ^{-2.5})$$ for our new estimates versus a standard particle filter that requires a work of $${\mathcal {O}}(\varepsilon ^{-3})$$ . Our theoretical results are supported by numerical simulations.
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Multilevel Particle Filters: Normalizing Constant Estimation
arXiv: Computation, 2016Co-Authors: Ajay Jasra, Kengo Kamatani, Peprah Osei, Yan ZhouAbstract:In this article we introduce two new estimates of the Normalizing Constant (or marginal likelihood) for partially observed diffusion (POD) processes, with discrete observations. One estimate is biased but non-negative and the other is unbiased but not almost surely non-negative. Our method uses the multilevel particle filter of Jasra et al (2015). We show that, under assumptions, for Euler discretized PODs and a given $\varepsilon>0$. in order to obtain a mean square error (MSE) of $\mathcal{O}(\varepsilon^2)$ one requires a work of $\mathcal{O}(\varepsilon^{-2.5})$ for our new estimates versus a standard particle filter that requires a work of $\mathcal{O}(\varepsilon^{-3})$. Our theoretical results are supported by numerical simulations.
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Error Bounds and Normalizing Constants for Sequential Monte Carlo in High Dimensions
arXiv: Computation, 2011Co-Authors: Alexandros Beskos, Ajay Jasra, Dan Crisan, Nick WhiteleyAbstract:In a recent paper Beskos et al (2011), the Sequential Monte Carlo (SMC) sampler introduced in Del Moral et al (2006), Neal (2001) has been shown to be asymptotically stable in the dimension of the state space d at a cost that is only polynomial in d, when N the number of Monte Carlo samples, is fixed. More precisely, it has been established that the effective sample size (ESS) of the ensuing (approximate) sample and the Monte Carlo error of fixed dimensional marginals will converge as $d$ grows, with a computational cost of $\mathcal{O}(Nd^2)$. In the present work, further results on SMC methods in high dimensions are provided as $d\to\infty$ and with $N$ fixed. We deduce an explicit bound on the Monte-Carlo error for estimates derived using the SMC sampler and the exact asymptotic relative $\mathbb{L}_2$-error of the estimate of the Normalizing Constant. We also establish marginal propagation of chaos properties of the algorithm. The accuracy in high-dimensions of some approximate SMC-based filtering schemes is also discussed.
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sequential monte carlo samplers
Journal of The Royal Statistical Society Series B-statistical Methodology, 2006Co-Authors: Pierre Del Moral, Arnaud Doucet, Ajay JasraAbstract:We propose a methodology to sample sequentially from a sequence of probability distributions that are defined on a common space, each distribution being known up to a Normalizing Constant. These probability distributions are approximated by a cloud of weighted random samples which are propagated over time by using sequential Monte Carlo methods. This methodology allows us to derive simple algorithms to make parallel Markov chain Monte Carlo algorithms interact to perform global optimization and sequential Bayesian estimation and to compute ratios of Normalizing Constants. We illustrate these algorithms for various integration tasks arising in the context of Bayesian inference. Copyright 2006 Royal Statistical Society.
Pierre Del Moral - One of the best experts on this subject based on the ideXlab platform.
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A lognormal central limit theorem for particle approximations of Normalizing Constants
Electronic Journal of Probability, 2014Co-Authors: Jean Bérard, Pierre Del Moral, Arnaud DoucetAbstract:Feynman-Kac path integration models arise in a large variety of scientic disciplines including physics, chemistry and signal processing. Their mean eld particle interpretations, termed Diusion or Quantum Monte Carlo methods in physics and Sequential Monte Carlo or Particle Filters in statistics and applied probability, have found numerous applications as they allow to sample approximately from sequences of complex probability distributions and estimate their associated Normalizing Constants.This article focuses on the lognormal fuctuations of these Normalizing Constant estimates when both the time horizon n and the number of particles N go to innity in such a way that n/N tends to some number between 0 and 1. To the best of our knowledge, this is the first result of this type for mean field type interacting particle systems. We also discuss special classes of models, including particle absorption models in time-homogeneous environment and hidden Markov models in ergodic random environment, for which more explicit descriptions of the limiting bias and variance can be obtained.
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sequential monte carlo samplers
Journal of The Royal Statistical Society Series B-statistical Methodology, 2006Co-Authors: Pierre Del Moral, Arnaud Doucet, Ajay JasraAbstract:We propose a methodology to sample sequentially from a sequence of probability distributions that are defined on a common space, each distribution being known up to a Normalizing Constant. These probability distributions are approximated by a cloud of weighted random samples which are propagated over time by using sequential Monte Carlo methods. This methodology allows us to derive simple algorithms to make parallel Markov chain Monte Carlo algorithms interact to perform global optimization and sequential Bayesian estimation and to compute ratios of Normalizing Constants. We illustrate these algorithms for various integration tasks arising in the context of Bayesian inference. Copyright 2006 Royal Statistical Society.
Arnaud Doucet - One of the best experts on this subject based on the ideXlab platform.
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A lognormal central limit theorem for particle approximations of Normalizing Constants
Electronic Journal of Probability, 2014Co-Authors: Jean Bérard, Pierre Del Moral, Arnaud DoucetAbstract:Feynman-Kac path integration models arise in a large variety of scientic disciplines including physics, chemistry and signal processing. Their mean eld particle interpretations, termed Diusion or Quantum Monte Carlo methods in physics and Sequential Monte Carlo or Particle Filters in statistics and applied probability, have found numerous applications as they allow to sample approximately from sequences of complex probability distributions and estimate their associated Normalizing Constants.This article focuses on the lognormal fuctuations of these Normalizing Constant estimates when both the time horizon n and the number of particles N go to innity in such a way that n/N tends to some number between 0 and 1. To the best of our knowledge, this is the first result of this type for mean field type interacting particle systems. We also discuss special classes of models, including particle absorption models in time-homogeneous environment and hidden Markov models in ergodic random environment, for which more explicit descriptions of the limiting bias and variance can be obtained.
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sequential monte carlo samplers
Journal of The Royal Statistical Society Series B-statistical Methodology, 2006Co-Authors: Pierre Del Moral, Arnaud Doucet, Ajay JasraAbstract:We propose a methodology to sample sequentially from a sequence of probability distributions that are defined on a common space, each distribution being known up to a Normalizing Constant. These probability distributions are approximated by a cloud of weighted random samples which are propagated over time by using sequential Monte Carlo methods. This methodology allows us to derive simple algorithms to make parallel Markov chain Monte Carlo algorithms interact to perform global optimization and sequential Bayesian estimation and to compute ratios of Normalizing Constants. We illustrate these algorithms for various integration tasks arising in the context of Bayesian inference. Copyright 2006 Royal Statistical Society.
Vladimir N. Minin - One of the best experts on this subject based on the ideXlab platform.
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19 dubious ways to compute the marginal likelihood of a phylogenetic tree topology
Systematic Biology, 2019Co-Authors: Mathieu Fourment, Andrew F. Magee, Chris Whidden, Arman Bilge, Frederick A. Matsen, Vladimir N. MininAbstract:Author(s): Fourment, Mathieu; Magee, Andrew F; Whidden, Chris; Bilge, Arman; Matsen, Frederick A; Minin, Vladimir N | Abstract: The marginal likelihood of a model is a key quantity for assessing the evidence provided by the data in support of a model. The marginal likelihood is the Normalizing Constant for the posterior density, obtained by integrating the product of the likelihood and the prior with respect to model parameters. Thus, the computational burden of computing the marginal likelihood scales with the dimension of the parameter space. In phylogenetics, where we work with tree topologies that are high-dimensional models, standard approaches to computing marginal likelihoods are very slow. Here, we study methods to quickly compute the marginal likelihood of a single fixed tree topology. We benchmark the speed and accuracy of 19 different methods to compute the marginal likelihood of phylogenetic topologies on a suite of real data sets under the JC69 model. These methods include several new ones that we develop explicitly to solve this problem, as well as existing algorithms that we apply to phylogenetic models for the first time. Altogether, our results show that the accuracy of these methods varies widely, and that accuracy does not necessarily correlate with computational burden. Our newly developed methods are orders of magnitude faster than standard approaches, and in some cases, their accuracy rivals the best established estimators.
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19 dubious ways to compute the marginal likelihood of a phylogenetic tree topology
arXiv: Populations and Evolution, 2018Co-Authors: Mathieu Fourment, Andrew F. Magee, Chris Whidden, Arman Bilge, Frederick A. Matsen, Vladimir N. MininAbstract:The marginal likelihood of a model is a key quantity for assessing the evidence provided by the data in support of a model. The marginal likelihood is the Normalizing Constant for the posterior density, obtained by integrating the product of the likelihood and the prior with respect to model parameters. Thus, the computational burden of computing the marginal likelihood scales with the dimension of the parameter space. In phylogenetics, where we work with tree topologies that are high-dimensional models, standard approaches to computing marginal likelihoods are very slow. Here we study methods to quickly compute the marginal likelihood of a single fixed tree topology. We benchmark the speed and accuracy of 19 different methods to compute the marginal likelihood of phylogenetic topologies on a suite of real datasets. These methods include several new ones that we develop explicitly to solve this problem, as well as existing algorithms that we apply to phylogenetic models for the first time. Altogether, our results show that the accuracy of these methods varies widely, and that accuracy does not necessarily correlate with computational burden. Our newly developed methods are orders of magnitude faster than standard approaches, and in some cases, their accuracy rivals the best established estimators.
Robert Reeves - One of the best experts on this subject based on the ideXlab platform.
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efficient calculation of the Normalizing Constant of the autologistic and related models on the cylinder and lattice
Journal of The Royal Statistical Society Series B-statistical Methodology, 2003Co-Authors: Anthony N Pettitt, Nial Friel, Robert ReevesAbstract:Motivated by the autologistic model for the analysis of spatial binary data on the two-dimensional lattice, we develop efficient computational methods for calculating the Normalizing Constant for models for discrete data defined on the cylinder and lattice. Because the Normalizing Constant is generally unknown analytically, statisticians have developed various ad hoc methods to overcome this difficulty. Our aim is to provide computationally and statistically efficient methods for calculating the Normalizing Constant so that efficient likelihood-based statistical methods are then available for inference. We extend the so-called transition method to find a feasible computational method of obtaining the Normalizing Constant for the cylinder boundary condition. To extend the result to the free-boundary condition on the lattice we use an efficient path sampling Markov chain Monte Carlo scheme. The methods are generally applicable to association patterns other than spatial, such as clustered binary data, and to variables taking three or more values described by, for example, Potts models.
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Efficient calculation of the Normalizing Constant of the autologistic and related models on the cylinder
2003Co-Authors: Anthony N Pettitt, Nial Friel, Robert ReevesAbstract:Summary. Motivated by the autologistic model for the analysis of spatial binary data on the two-dimensional lattice, we develop efficient computational methods for calculating the Normalizing Constant for models for discrete data defined on the cylinder and lattice. Because the Normalizing Constant is generally unknown analytically, statisticians have developed various ad hoc methods to overcome this difficulty. Our aim is to provide computationally and statistically efficient methods for calculating the Normalizing Constant so that efficient likelihood-based statistical methods are then available for inference. We extend the so-called transition method to find a feasible computational method of obtaining the Normalizing Constant for the cylinder boundary condition. To extend the result to the free-boundary condition on the lattice we use an efficient path sampling Markov chain Monte Carlo scheme. The methods are generally applicable to association patterns other than spatial, such as clustered binary data, and to variables taking three or more values described by, for example, Potts models.