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Article
Open AccessMulti-index Sequential Monte Carlo Ratio Estimators for Bayesian Inverse problems
We consider the problem of estimating expectations with respect to a target distribution with an unknown normalising constant, and where even the un-normalised target needs to be approximated at finite resolut...
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Article
Open AccessA 4D-Var method with flow-dependent background covariances for the shallow-water equations
The 4D-Var method for filtering partially observed nonlinear chaotic dynamical systems consists of finding the maximum a-posteriori (MAP) estimator of the initial condition of the system given observations ove...
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Article
Open AccessUncertainty modelling and computational aspects of data association
A novel solution to the smoothing problem for multi-object dynamical systems is proposed and evaluated. The systems of interest contain an unknown and varying number of dynamical objects that are partially obs...
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Article
Open AccessUnbiased estimation of the gradient of the log-likelihood in inverse problems
We consider the problem of estimating a parameter \(\theta \in \Theta \subseteq {\mathbb {R}}^{d_{\theta }}\) ...
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Article
Open AccessCorrection to: Multilevel particle filters for Lévy-driven stochastic differential equations
The article Multilevel particle filters for Lévy-driven stochastic differential equations, written by Ajay Jasra, Kody J. H. Law, Prince Peprah Osei, was originally published electronically on the publisher’s ...
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Article
Open AccessMultilevel particle filters for Lévy-driven stochastic differential equations
We develop algorithms for computing expectations with respect to the laws of models associated to stochastic differential equations driven by pure Lévy processes. We consider filtering such processes as well a...
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Article
Open AccessOptimization Based Methods for Partially Observed Chaotic Systems
In this paper we consider filtering and smoothing of partially observed chaotic dynamical systems that are discretely observed, with an additive Gaussian noise in the observation. These models are found in a w...
