On the stability of interacting processes with applications to filtering and geneticÂ algorithms

Moral, Pierre Del; Guionnet, Alice

doi:10.1016/s0246-0203(00)01064-5

Cited by 168 publications

(198 citation statements)

References 24 publications

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“…See details on constants C and α in Del Moral and Guionnet [7]. Here p N ( · | · ) denotes the particle representation of the full density p( · | · ).…”

Section: Convergence Of Particle Filters To the Target Densitymentioning

confidence: 99%

Particle Filters for nonlinear data assimilation in high-dimensional systems

Leeuwen¹,

Jan²

2017

Annales De La Faculté Des Sciences De Toulouse : Mathématiques

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“…See details on constants C and α in Del Moral and Guionnet [7]. Here p N ( · | · ) denotes the particle representation of the full density p( · | · ).…”

Section: Convergence Of Particle Filters To the Target Densitymentioning

confidence: 99%

Particle Filters for nonlinear data assimilation in high-dimensional systems

Leeuwen¹,

Jan²

2017

Annales De La Faculté Des Sciences De Toulouse : Mathématiques

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“…Notice that the choice of M does not affect the convergence of the particle filter algorithms, which depends only on the choice of N . 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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“…The Monte Carlo particle filter is an SMC method that does not have a branching mechanism. For the required filter stability, it suffices to have mixing or ergodic signal kernels [1], [5]. In [14], the uniform convergence of the Monte Carlo filter has been extended to the estimation of parameters whose kernels are not mixing.…”

Section: Introductionmentioning

confidence: 99%

“…In [14], the uniform convergence of the Monte Carlo filter has been extended to the estimation of parameters whose kernels are not mixing. It has also been shown in [5] that the mixing property or the ergodicity of the signal kernel are sufficient conditions for the uniform convergence of the interacting particle system, which in contrast to the Monte Carlo particle filter has interacting particles because of the incorporated branching mechanism. A somewhat different approach can be found in [10], where the uniform convergence of a rejection-sampling-based particle filter has been considered in the case of a mixing signal.…”

Section: Introductionmentioning

confidence: 99%

Uniform approximations of discrete-time filters

Heine

Crisan

2008

Adv. Appl. Probab.

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Throughout recent years, various sequential Monte Carlo methods, i.e. particle filters, have been widely applied to various applications involving the evaluation of the generally intractable stochastic discrete-time filter. Although convergence results exist for finitetime intervals, a stronger form of convergence, namely, uniform convergence, is required for bounding the error on an infinite-time interval. In this paper we prove easily verifiable conditions for the filter applications that are sufficient for the uniform convergence of certain particle filters. Essentially, the conditions require the observations to be accurate enough. No mixing or ergodicity conditions are imposed on the signal process.

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On the stability of interacting processes with applications to filtering and geneticÂ algorithms

Cited by 168 publications

References 24 publications

Particle Filters for nonlinear data assimilation in high-dimensional systems

Particle Filters for nonlinear data assimilation in high-dimensional systems

Parallel Sequential Monte Carlo for Efficient Density Combination: TheDeCoMATLABToolbox

Uniform approximations of discrete-time filters

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