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31
Sequential Monte Carlo Samplers
, 2002
"... In this paper, we propose a general algorithm to sample sequentially from a sequence of probability distributions known up to a normalizing constant and defined on a common space. A sequence of increasingly large artificial joint distributions is built; each of these distributions admits a marginal ..."
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Cited by 303 (44 self)
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In this paper, we propose a general algorithm to sample sequentially from a sequence of probability distributions known up to a normalizing constant and defined on a common space. A sequence of increasingly large artificial joint distributions is built; each of these distributions admits a marginal which is a distribution of interest. To sample from these distributions, we use sequential Monte Carlo methods. We show that these methods can be interpreted as interacting particle approximations of a nonlinear FeynmanKac flow in distribution space. One interpretation of the FeynmanKac flow corresponds to a nonlinear Markov kernel admitting a specified invariant distribution and is a natural nonlinear extension of the standard MetropolisHastings algorithm. Many theoretical results have already been established for such flows and their particle approximations. We demonstrate the use of these algorithms through simulation.
A tutorial on particle filtering and smoothing: fifteen years later
 OXFORD HANDBOOK OF NONLINEAR FILTERING
, 2011
"... Optimal estimation problems for nonlinear nonGaussian statespace models do not typically admit analytic solutions. Since their introduction in 1993, particle filtering methods have become a very popular class of algorithms to solve these estimation problems numerically in an online manner, i.e. r ..."
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Cited by 214 (15 self)
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Optimal estimation problems for nonlinear nonGaussian statespace models do not typically admit analytic solutions. Since their introduction in 1993, particle filtering methods have become a very popular class of algorithms to solve these estimation problems numerically in an online manner, i.e. recursively as observations become available, and are now routinely used in fields as diverse as computer vision, econometrics, robotics and navigation. The objective of this tutorial is to provide a complete, uptodate survey of this field as of 2008. Basic and advanced particle methods for filtering as well as smoothing are presented.
Bayesian parameter inference for stochastic biochemical network models using particle Markov chain Monte Carlo
, 2011
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A sequential smoothing algorithm with linear computational cost
, 2008
"... In this paper we propose a new particle smoother that has a computational complexity of O(N), where N is the number of particles. This compares favourably with the O(N 2) computational cost of most smoothers and will result in faster rates of convergence for fixed computational cost. The new method ..."
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Cited by 33 (2 self)
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In this paper we propose a new particle smoother that has a computational complexity of O(N), where N is the number of particles. This compares favourably with the O(N 2) computational cost of most smoothers and will result in faster rates of convergence for fixed computational cost. The new method also overcomes some of the degeneracy problems we identify in many existing algorithms. Through simulation studies we show that substantial gains in efficiency are obtained for practical amounts of computational cost. It is shown both through these simulation studies, and on the analysis of an athletics data set, that our new method also substantially outperforms the simple FilterSmoother (the only other smoother with computational cost that is linear in the number of particles). 1
Adaptive Methods for Sequential Importance Sampling with Application to State Space Models.
, 2008
"... Abstract. In this note we discuss new adaptive proposal strategies for sequential Monte Carlo algorithmsalso known as particle filtersrelying on new criteria evaluating the quality of the proposed particles. The choice of the proposal distribution is of major concern and can dramatically influenc ..."
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Cited by 25 (6 self)
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Abstract. In this note we discuss new adaptive proposal strategies for sequential Monte Carlo algorithmsalso known as particle filtersrelying on new criteria evaluating the quality of the proposed particles. The choice of the proposal distribution is of major concern and can dramatically influence the quality of the estimates. Thus, we show how the longused coefficient of variation of the weights, suggested by
Particle Filtering and Smoothing: Fifteen years Later, Handbook of Nonlinear Filtering
"... Optimal estimation problems for nonlinear nonGaussian statespace models do not typically admit finitedimensional solutions. Since their introduction in 1993, particle filtering methods have become a very popular class of algorithms to solve these estimation problems numerically in an online mann ..."
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Cited by 7 (0 self)
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Optimal estimation problems for nonlinear nonGaussian statespace models do not typically admit finitedimensional solutions. Since their introduction in 1993, particle filtering methods have become a very popular class of algorithms to solve these estimation problems numerically in an online manner (that is, recursively, as observations become available), and are now routinely used in fields as diverse as computer vision, econometrics, robotics and navigation. The objective of this tutorial is to provide a complete, uptodate survey of this field as of 2008. Basic and advanced particle methods for filtering as well as smoothing are presented.
Efficient Bayesian analysis of multiple changepoint models with dependence across segments
, 2010
"... We consider Bayesian analysis of a class of multiple changepoint models. While there are a variety of efficient ways to analyse these models if the parameters associated with each segment are independent, there are few general approaches for models where the parameters are dependent. Under the assu ..."
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Cited by 6 (0 self)
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We consider Bayesian analysis of a class of multiple changepoint models. While there are a variety of efficient ways to analyse these models if the parameters associated with each segment are independent, there are few general approaches for models where the parameters are dependent. Under the assumption that the dependence is Markov, we propose an efficient online algorithm for sampling from an approximation to the posterior distribution of the number and position of the changepoints. In a simulation study, we show that the approximation introduced is negligible. We illustrate the power of our approach through fitting piecewise polynomial models to data, under a model which allows for either continuity or discontinuity of the underlying curve at each changepoint. This method is competitive with, or outperforms, other methods for inferring curves from noisy data; and uniquely it allows for inference of the locations of discontinuities in the underlying curve.
Markov and semiMarkov switching linear mixed models for identifying forest tree growth components
 n o 6618, INRIA, 2008, http://wwwsop.inria.fr/virtualplants/Publications/2008/CGLT08. Virtual Plants 29
"... 2 Markov and semiMarkov switching linear mixed models used to identify forest tree growth components ..."
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Cited by 5 (0 self)
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2 Markov and semiMarkov switching linear mixed models used to identify forest tree growth components
Guided proposals for simulating multidimensional diffusion bridges
"... A Monte Carlo method for simulating a multidimensional diffusion process conditioned on hitting a fixed point at a fixed future time is developed. Proposals for such diffusion bridges are obtained by superimposing an additional guiding term to the drift of the process under consideration. The gui ..."
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Cited by 3 (0 self)
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A Monte Carlo method for simulating a multidimensional diffusion process conditioned on hitting a fixed point at a fixed future time is developed. Proposals for such diffusion bridges are obtained by superimposing an additional guiding term to the drift of the process under consideration. The guiding term is derived via approximation of the target process by a simpler diffusion processes with known transition densities. Acceptance of a proposal can be determined by computing the likelihood ratio between the proposal and the target bridge, which is derived in closed form. We show under general conditions that the likelihood ratio is well defined and show that a class of proposals with guiding term obtained from linear approximations fall under these conditions. This is illustrated numerically in a twodimensional example.