A nonasymptotic theorem for unnormalized Feynman–Kac particle models

Cérou, Frédéric; Moral, Pierre Del; Guyader, Arnaud

doi:10.1214/10-aihp358

Cited by 104 publications

(168 citation statements)

References 8 publications

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“…Other related work is that of Cerou et al (2011) who use a sequence of decreasing sets to enter a desirable set in the context of rare event probability estimation. We showcase a general constraint enforcement strategy as well as application specific strategies.…”

Section: Sequences Of Densitiesmentioning

confidence: 99%

Sequentially Constrained Monte Carlo

Golchi

Campbell

2016

Computational Statistics & Data Analysis

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a b s t r a c tConstraints can be interpreted in a broad sense as any kind of explicit restriction over the parameters. While some constraints are defined directly on the parameter space, when they are instead defined by known behavior on the model, transformation of constraints into features on the parameter space may not be possible. Incorporation of constraints into the model often leads to truncations in the parameter space and multimodality which in turn cause difficulties in posterior sampling. A variant of the Sequential Monte Carlo algorithm is proposed by defining a sequence of densities through the imposition of the constraint. Particles generated from an unconstrained or mildly constrained distribution are filtered and moved through sampling and resampling steps to obtain a sample from the fully constrained target distribution. General and model specific forms of constraints enforcing strategies are defined. The Sequentially Constrained Monte Carlo algorithm is demonstrated on constraints defined by monotonicity of a function, densities constrained to low dimensional manifolds, adherence to a mechanistic differential equation model, and Approximate Bayesian Computation.Crown

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Section: Sequences Of Densitiesmentioning

confidence: 99%

Sequentially Constrained Monte Carlo

Golchi

Campbell

2016

Computational Statistics & Data Analysis

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“…See for instance Corollary 4.3.3. in [7] and the more recent article [4]. On the other hand, let us suppose that…”

Section: Theorem 32 For Anymentioning

confidence: 99%

A backward particle interpretation of Feynman-Kac formulae

2010

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Abstract. We design a particle interpretation of Feynman-Kac measures on path spaces based on a backward Markovian representation combined with a traditional mean field particle interpretation of the flow of their final time marginals. In contrast to traditional genealogical tree based models, these new particle algorithms can be used to compute normalized additive functionals "on-the-fly" as well as their limiting occupation measures with a given precision degree that does not depend on the final time horizon. We provide uniform convergence results w.r.t. the time horizon parameter as well as functional central limit theorems and exponential concentration estimates, yielding what seems to be the first results of this type for this class of models. We also illustrate these results in the context of filtering of hidden Markov models, as well as in computational physics and imaginary time Schroedinger type partial differential equations, with a special interest in the numerical approximation of the invariant measure associated to h-processes.Mathematics Subject Classification. 65C05, 65C35, 60G35, 47D08.

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“…For higher probabilities, other simulation methods as IS are more efficient than AST [116]. The logarithmic efficiency has been proved for splitting with fixed levels in [118].…”

Section: Necessary Simulation Budget Restrictedmentioning

confidence: 98%

A survey of rare event simulation methods for static input–output models

Mitard

Balesdent

Jacquemart

et al. 2014

Simulation Modelling Practice and Theory

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International audienceCrude Monte-Carlo or quasi Monte-Carlo methods are well suited to characterize events of which associated probabilities are not too low with respect to the simulation budget. For very seldom observed events, such as the collision probability between two aircraft in airspace, these approaches do not lead to accurate results. Indeed, the number of available samples is often insufficient to estimate such low probabilities (at least 10^6 samples are needed to estimate a probability of order 10^-4with 10% relative error with Monte-Carlo simulations). In this article, one reviewed different appropriate techniques to estimate rare event probabilities that require a fewer number of samples. These methods can be divided into four main categories: parameterization techniques of probability density function tails, simulation techniques such as importance sampling or importance splitting, geometric methods to approximate input failure space and finally, surrogate modeling. Each technique is detailed, its advantages and drawbacks are described and a synthesis that aims at giving some clues to the following question is given: “which technique to use for which problem?”

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A nonasymptotic theorem for unnormalized Feynman–Kac particle models

Cited by 104 publications

References 8 publications

Sequentially Constrained Monte Carlo

Sequentially Constrained Monte Carlo

A backward particle interpretation of Feynman-Kac formulae

A survey of rare event simulation methods for static input–output models

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