A general theory of particle filters in hidden Markov models and some applications

Chan, Hock Peng; Lai, Tze Leung

doi:10.1214/13-aos1172

Cited by 65 publications

(54 citation statements)

References 13 publications

(40 reference statements)

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“…The variance estimator (28) for Quantile DMC was originally developed assuming a different resampling scheme called Bernoulli resampling is used 33 . Indeed, when the DMC algorithm is performed using Bernoulli resampling, the variance estimator is asympotically consistent as N → ∞.…”

Section: Variance Estimation For Quantile Dmcmentioning

confidence: 99%

Practical rare event sampling for extreme mesoscale weather

Webber

Plotkin

O’Neill

et al. 2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Extreme mesoscale weather, including tropical cyclones, squall lines, and floods, can be enormously damaging and yet challenging to simulate; hence, there is a pressing need for more efficient simulation strategies. Here we present a new rare event sampling algorithm called Quantile Diffusion Monte Carlo (Quantile DMC). Quantile DMC is a simple-to-use algorithm that can sample extreme tail behavior for a wide class of processes. We demonstrate the advantages of Quantile DMC compared to other sampling methods and discuss practical aspects of implementing Quantile DMC. To test the feasibility of Quantile DMC for extreme mesoscale weather, we sample extremely intense realizations of two historical tropical cyclones, 2010 Hurricane Earl and 2015 Hurricane Joaquin. Our results demonstrate Quantile DMC's potential to provide low-variance extreme weather statistics while highlighting the work that is necessary for Quantile DMC to attain greater efficiency in future applications.

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Section: Variance Estimation For Quantile Dmcmentioning

confidence: 99%

Practical rare event sampling for extreme mesoscale weather

Webber

Plotkin

O’Neill

et al. 2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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show abstract

“…A more informative class of results consists in central limit theorem equivalents of Equation (16). These results can be used to assess the total variance of Monte Carlo estimators (whereas measures such as effective sample size described previously are local in nature), see Chan and Lai (2013). However, since numerically stable versions of these methods are still at their infancy (Olsson and Douc 2017), we will focus the remaining on the third property, unbiasedness.…”

Section: Properties Of Annealed Sequential Monte Carlomentioning

confidence: 99%

An Annealed Sequential Monte Carlo Method for Bayesian Phylogenetics

Wang

Bouchard‐Côté

2019

Systematic Biology

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We describe an "embarrassingly parallel" method for Bayesian phylogenetic inference, annealed Sequential Monte Carlo, based on recent advances in the Sequential Monte Carlo literature such as adaptive determination of annealing parameters. The algorithm provides an approximate posterior distribution over trees and evolutionary parameters as well as an unbiased estimator for the marginal likelihood. This unbiasedness property can be used for the purpose of testing the correctness of posterior simulation software. We evaluate the performance of phylogenetic annealed Sequential Monte Carlo by reviewing and comparing with other computational Bayesian phylogenetic methods, in particular, different marginal likelihood estimation methods.Unlike previous Sequential Monte Carlo methods in phylogenetics, our annealed method can utilize standard Markov chain Monte Carlo tree moves and hence benefit from the large inventory of such moves available in the literature. Consequently, the annealed Sequential Monte Carlo method should be relatively easy to incorporate into existing phylogenetic software packages based on Markov chain Monte Carlo algorithms. We illustrate our method using simulation studies and real data analysis.

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“…The assumptions required for convergence of the SMC algorithms are discussed in, e.g., Moral and Guionnet (2001) and Gland and Oudjane (2004) for regularized particle filters. Central limit theorems for particle filters can be found in Chan and Lai (2013) and Chopin (2004).…”

Section: (Observation Marginal Predictive Equation 13)mentioning

confidence: 99%

Parallel Sequential Monte Carlo for Efficient Density Combination: TheDeCoMATLABToolbox

Casarin¹,

Grassi²,

Ravazzolo³

et al. 2015

J. Stat. Soft.

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This paper presents the MATLAB package DeCo (density combination) which is based on the paper by Billio, Casarin, Ravazzolo, and van Dijk (2013) where a constructive Bayesian approach is presented for combining predictive densities originating from different models or other sources of information. The combination weights are time-varying and may depend on past predictive forecasting performances and other learning mechanisms. The core algorithm is the function DeCo which applies banks of parallel sequential Monte Carlo algorithms to filter the time-varying combination weights. The DeCo procedure has been implemented both for standard CPU computing and for graphical process unit (GPU) parallel computing. For the GPU implementation we use the MATLAB parallel computing toolbox and show how to use general purpose GPU computing almost effortlessly. This GPU implementation provides a speed-up of the execution time of up to seventy times on a standard CPU MATLAB implementation on a multicore CPU. We show the use of the package and the computational gain of the GPU version through some simulation experiments and empirical applications.

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A general theory of particle filters in hidden Markov models and some applications

Cited by 65 publications

References 13 publications

Practical rare event sampling for extreme mesoscale weather

Practical rare event sampling for extreme mesoscale weather

An Annealed Sequential Monte Carlo Method for Bayesian Phylogenetics

Parallel Sequential Monte Carlo for Efficient Density Combination: TheDeCoMATLABToolbox

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