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42
Sequential Monte Carlo Methods for Dynamic Systems
 Journal of the American Statistical Association
, 1998
"... A general framework for using Monte Carlo methods in dynamic systems is provided and its wide applications indicated. Under this framework, several currently available techniques are studied and generalized to accommodate more complex features. All of these methods are partial combinations of three ..."
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Cited by 650 (12 self)
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A general framework for using Monte Carlo methods in dynamic systems is provided and its wide applications indicated. Under this framework, several currently available techniques are studied and generalized to accommodate more complex features. All of these methods are partial combinations of three ingredients: importance sampling and resampling, rejection sampling, and Markov chain iterations. We deliver a guideline on how they should be used and under what circumstance each method is most suitable. Through the analysis of differences and connections, we consolidate these methods into a generic algorithm by combining desirable features. In addition, we propose a general use of RaoBlackwellization to improve performances. Examples from econometrics and engineering are presented to demonstrate the importance of RaoBlackwellization and to compare different Monte Carlo procedures. Keywords: Blind deconvolution; Bootstrap filter; Gibbs sampling; Hidden Markov model; Kalman filter; Markov...
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 de ned on a common space. A sequence of increasingly large arti cial joint distributions is built; each of these distributions admits a marginal ..."
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Cited by 311 (48 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 de ned on a common space. A sequence of increasingly large arti cial 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 ow in distribution space. One interpretation of the FeynmanKac ow corresponds to a nonlinear Markov kernel admitting a speci ed invariant distribution and is a natural nonlinear extension of the standard MetropolisHastings algorithm. Many theoretical results have already been established for such ows and their particle approximations. We demonstrate the use of these algorithms through simulation.
Computational Methods for Complex Stochastic Systems: A Review of Some Alternatives to MCMC
"... We consider analysis of complex stochastic models based upon partial information. MCMC and reversible jump MCMC are often the methods of choice for such problems, but in some situations they can be difficult to implement; and suffer from problems such as poor mixing, and the difficulty of diagnosing ..."
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Cited by 34 (5 self)
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We consider analysis of complex stochastic models based upon partial information. MCMC and reversible jump MCMC are often the methods of choice for such problems, but in some situations they can be difficult to implement; and suffer from problems such as poor mixing, and the difficulty of diagnosing convergence. Here we review three alternatives to MCMC methods: importance sampling, the forwardbackward algorithm, and sequential Monte Carlo (SMC). We discuss how to design good proposal densities for importance sampling, show some of the range of models for which the forwardbackward algorithm can be applied, and show how resampling ideas from SMC can be used to improve the efficiency of the other two methods. We demonstrate these methods on a range of examples, including estimating the transition density of a diffusion and of a discretestate continuoustime Markov chain; inferring structure in population genetics; and segmenting genetic divergence data.
Resampling Algorithms for Particle Filters: A Computational Complexity Perspective
"... Newly developed resampling algorithms for particle filters suitable for realtime implementation are described and their analysis is presented. The new algorithms reduce the complexity of both hardware and DSP realization through addressing common issues such as decreasing the number of operations a ..."
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Cited by 24 (2 self)
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Newly developed resampling algorithms for particle filters suitable for realtime implementation are described and their analysis is presented. The new algorithms reduce the complexity of both hardware and DSP realization through addressing common issues such as decreasing the number of operations and memory access. Moreover, the algorithms allow for use of higher sampling frequencies by overlapping in time the resampling step with the other particle filtering steps. Since resampling is not dependent on any particular application, the analysis is appropriate for all types of particle filters that use resampling. The performance of the algorithms is evaluated on particle filters applied to bearingsonly tracking and joint detection and estimation in wireless communications. We have demonstrated that the proposed algorithms reduce the complexity without performance degradation. Key words: particle filters, resampling, computational complexity, sequential implementation 1
Architectures for Efficient Implementation of Particle Filters
, 2004
"... Particle filters are sequential Monte Carlo methods that are used in numerous problems where timevarying signals must be presented in real time and where the objective is to estimate various unknowns of the signal and/or detect events described by the signals. The standard solutions of such proble ..."
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Cited by 22 (0 self)
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Particle filters are sequential Monte Carlo methods that are used in numerous problems where timevarying signals must be presented in real time and where the objective is to estimate various unknowns of the signal and/or detect events described by the signals. The standard solutions of such problems in many applications are based on the Kalman filters or extended Kalman filters. In situations when the problems are nonlinear or the noise that distorts the signals is nonGaussian, the Kalman filters provide a solution that may be far from optimal. Particle filters are an intriguing alternative to the Kalman filters due to their excellent performance in very di#cult problems including communications, signal processing, navigation, and computer vision. Hence, particle filters have been the focus of wide research recently and immense literature can be found on their theory. Most of these works recognize the complexity and computational intensity of these filters, but there has been no e#ort directed toward the implementation of these filters in hardware. The objective of this dissertation is to develop, design, and build e#cient hardware for particle filters, and thereby bring them closer to practical applications. The fact that particle filters outperform most of the traditional filtering methods in many complex practical scenarios, coupled with the challenges related to decreasing their computational complexity and improving realtime performance, makes this work worthwhile. The main
On sequential Monte Carlo, partial rejection control and approximate Bayesian computation
, 2008
"... We present a sequential Monte Carlo sampler variant of the partial rejection control algorithm introduced by Liu (2001), termed SMC sampler PRC, and show that this variant can be considered under the same framework of the sequential Monte Carlo sampler of Del Moral et al. (2006). We make connections ..."
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Cited by 19 (6 self)
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We present a sequential Monte Carlo sampler variant of the partial rejection control algorithm introduced by Liu (2001), termed SMC sampler PRC, and show that this variant can be considered under the same framework of the sequential Monte Carlo sampler of Del Moral et al. (2006). We make connections with existing algorithms and theoretical results, and extend some theoretical results to the SMC sampler PRC setting. We examine the properties of the SMC sampler PRC and give recommendations for user specified quantities. We also study the special case of SMC sampler PRC in the “likelihood free” approximate Bayesian computation framework, as introduced by Sisson et al. (2007).
Computing Normalizing Constants for Finite Mixture Models via Incremental Mixture Importance Sampling (IMIS)
, 2003
"... We propose a method for approximating integrated likelihoods in finite mixture models. We formulate the model in terms of the unobserved group memberships, z, and make them the variables of integration. The integral is then evaluated using importance sampling over the z. We propose an adaptive imp ..."
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Cited by 15 (5 self)
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We propose a method for approximating integrated likelihoods in finite mixture models. We formulate the model in terms of the unobserved group memberships, z, and make them the variables of integration. The integral is then evaluated using importance sampling over the z. We propose an adaptive importance sampling function which is itself a mixture, with two types of component distributions, one concentrated and one diffuse. The more concentrated type of component serves the usual purpose of an importance sampling function, sampling mostly group assignments of high posterior probability. The less concentrated type of component allows for the importance sampling function to explore the space in a controlled way to find other, unvisited assignments with high posterior probability. Components are added adaptively, one at a time, to cover areas of high posterior probability not well covered by the current important sampling function. The method is called Incremental Mixture Importance Sampling (IMIS). IMIS is easy to implement and to monitor for convergence. It scales easily for higher dimensional
Stochastic Neural Networks with Applications to Nonlinear Time Series
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 2001
"... Neural networks have a burgeoning literature in nonlinear time series. We consider here a variant of the conventional neural network model, called the stochastic neural network, that can be used to approximate complex nonlinear stochastic systems. We show how the EM algorithm can be used to develop ..."
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Cited by 9 (2 self)
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Neural networks have a burgeoning literature in nonlinear time series. We consider here a variant of the conventional neural network model, called the stochastic neural network, that can be used to approximate complex nonlinear stochastic systems. We show how the EM algorithm can be used to develop efficient estimation schemes that have much lower computational complexity than those for conventional neural networks. This enables us to carry out model selection procedures such as the BIC to choose the number of hidden units and the input variables for each hidden unit. On the other hand, stochastic neural networks are shown to have the universal approximation property of neural networks. Other important properties of the proposed model are also given, and modelbased multistep ahead forecasts are provided. For illustration, we fit stochastic neural network models to several real and simulated time series. Our results show that the fitted models improve postsample forecasts over conventional neural networks and other nonlinear/nonparametric models.
A statistical perspective on algorithmic leveraging
, 2013
"... One popular method for dealing with largescale data sets is sampling. Using the empirical statistical leverage scores as an importance sampling distribution, the method of algorithmic leveraging samples and rescales data matrices to reduce the data size before performing computations on the subpr ..."
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Cited by 8 (1 self)
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One popular method for dealing with largescale data sets is sampling. Using the empirical statistical leverage scores as an importance sampling distribution, the method of algorithmic leveraging samples and rescales data matrices to reduce the data size before performing computations on the subproblem. Existing work has focused on algorithmic issues, but none of it addresses statistical aspects of this method. Here, we provide an effective framework to evaluate the statistical properties of algorithmic leveraging in the context of estimating parameters in a linear regression model. In particular, for several versions of leveragebased sampling, we derive results for the bias and variance. We show that from the statistical perspective of bias and variance, neither leveragebased sampling nor uniform sampling dominates the other. This result is particularly striking, given the wellknown result that, from the algorithmic perspective of worstcase analysis, leveragebased sampling provides uniformly superior worstcase algorithmic results, when compared with uniform sampling. Based on these theoretical results, we propose and analyze two new leveraging algorithms: one constructs a smaller leastsquares problem with “shrinked” leverage scores (SLEV), and the other solves a smaller and unweighted (or biased) leastsquares problem (LEVUNW). The empirical results indicate that our theory is a good predictor of practical performance of existing and new leveragebased algorithms and that the new algorithms achieve improved performance.
Online inference for multiple change points problems
 Journal of the Royal Statistical Society B
, 2007
"... We propose an online algorithm for exact filtering of multiple changepoint problems. This algorithm enables simulation from the true joint posterior distribution of the number and position of the changepoints for a class of changepoint models. The computational cost of this exact algorithm is qua ..."
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Cited by 8 (0 self)
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We propose an online algorithm for exact filtering of multiple changepoint problems. This algorithm enables simulation from the true joint posterior distribution of the number and position of the changepoints for a class of changepoint models. The computational cost of this exact algorithm is quadratic in the number of observations. We further show how resampling ideas from particle filters can be used to reduce the computational cost to linear in the number of observations, at the expense of introducing small errors; and propose two new, optimum resampling algorithms for this problem. One, a version of rejection control, allows the particle filter to automatically choose the number of particles required at each timestep. The new resampling algorithms substantially outperform standard resampling algorithms on examples we consider; and we demonstrate how the resulting particle filter is practicable for segmentation of human GC content.