Branching and interacting particle systems. Approximations of Feynman-Kac formulae with applications to non-linear filtering

By Pierre Del Moral, Laurent Miclo. 2000

333 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Mathematical Physics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/d572a501cf98db4f88a2fd4a7f681e338b2208df

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Citations in the corpus

On contraction properties of Markov kernels (2003, background): “Indeed, it is not difficult to choose a “wild” sequence (an)n≥0 which will not allow for this convergence (and such an occurrence is not only theoretical, as it often appears in the context of linear and nonlinear filtering [ 6 ]).”
A survey of convergence results on particle filtering methods for practitioners (2002, methodology): “This is by no way an exhaustive list of results; see, for example, [10] for further detailed results and their proofs.”
Central limit theorem for sequential Monte Carlo methods and its application to Bayesian inference (2004, result): “No assumption is made on the model that generates the sequence of distributions of interest (πt), so that our theorem equally applies to those recent algorithms [Chopin (2002), Del Moral and Doucet (2002) and Cappé, Guillin, Marin and Robert (2004)] that have been developed for contexts that widely”
Adapting the Sample Size in Particle Filters Through KLD-Sampling (2003, methodology): “Furthermore, the sample-based posterior converges to the true posterior at a rate of 1/ √ n as the number n of samples goes to infinity (Del Moral and Miclo 2000).”
Exponential convergence to quasi-stationary distribution and Q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Q$$\end{ (2014, neutral): “We also refer the reader to [16, 17, 18] for approximations techniques of non absorbed trajectories in terms of genealogical trees.”
Sequential Monte Carlo samplers (2002, methodology): “R b P If π n = π , then the following estimate can be also used e Though the particles are statistically dependent, one can show under assumptions given in (Del Moral and Miclo, 2000) that this estimate is consistent as N → ∞ .”
Inferring High-Level Behavior from Low-Level Sensors (2003, methodology): “It can be shown that this procedure in fact approximates the Bayes filter update (1), using a sample-based representation [7,13].”
Nonparametric estimation of diffusions: a differential equations approach (2012, background): “…with error, either via conditionally independent noisy observations, or via a discretely observed continuous-time process whose drift depends on the diffusion; these are versions of the so-called non-linear filtering problem, see for example Del Moral & Miclo (2000); Fearnhead et al. (2010).”
Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime (2004, positive): “The proof is adapted from Del Moral and Guionnet (2001) [see also Del Moral and Miclo (2000)].”
Approximate McKean–Vlasov representations for a class of SPDEs (2005, methodology): “For an extensive account of these methods in the general context of approximating Feynman-Kač operators of the type (11), see Del Moral [8] and Del Moral and Miclo [9].”
Particle filters for partially observed diffusions (2007, background): “The resulting particle filter has good theoretical properties including consistency (Crisan, 2001) and CLTs for estimates of posterior moments (Del Moral and Miclo, 2000; Chopin, 2004; Künsch, 2005), as N →∞.”
Inference for Lévy‐Driven Stochastic Volatility Models via Adaptive Sequential Monte Carlo (2011, methodology): “(2004) who fit SV models with the changes in the log price modelled via a driftless diffusion and volatilities through a super-position of OU processes with Gamma marginals (see also Del Moral et al., 2007 for sequential inference for this model); Griffin & Steel (2006) who, in addition, investigate”
Robust filtering: Correlated noise and multidimensional observation (2012, background): “In this case the filtering problem is well understood and has been studied in many works, including the monograph [16] and the articles [18, 17, 19].”