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Article
Open AccessFast deep mixtures of Gaussian process experts
Mixtures of experts have become an indispensable tool for flexible modelling in a supervised learning context, allowing not only the mean function but the entire density of the output to change with the inputs...
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Article
Open AccessA randomized multi-index sequential Monte Carlo method
We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resoluti...
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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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Chapter and Conference Paper
Randomized Multilevel Monte Carlo for Embarrassingly Parallel Inference
This position paper summarizes a recently developed research program focused on inference in the context of data centric science and engineering applications, and forecasts its trajectory forward over the next...
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Article
Open AccessA Bayesian analysis of classical shadows
The method of classical shadows proposed by Huang, Kueng, and Preskill heralds remarkable opportunities for quantum estimation with limited measurements. Yet its relationship to established quantum tomographic...
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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 AccessMultilevel ensemble Kalman filtering for spatio-temporal processes
We design and analyse the performance of a multilevel ensemble Kalman filter method (MLEnKF) for filtering settings where the underlying state-space model is an infinite-dimensional spatio-temporal process. We...
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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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Chapter
Bayesian Point Set Registration
Point set registration involves identifying a smooth invertible transformation between corresponding points in two point sets, one of which may be smaller than the other and possibly corrupted by observation n...
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Article
Determining white noise forcing from Eulerian observations in the Navier-Stokes equation
The Bayesian approach to inverse problems is of paramount importance in quantifying uncertainty about the input to, and the state of, a system of interest given noisy observations. Herein we consider the forwa...
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Article
Evaluation of Gaussian approximations for data assimilation in reservoir models
The Bayesian framework is the standard approach for data assimilation in reservoir modeling. This framework involves characterizing the posterior distribution of geological parameters in terms of a given prior...
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Chapter
The Dynamics of Unstable Waves
Discretized equations in which the evolution variable is continuous while the spatial variables are confined to the points on a lattice, have had a significant presence and impact across multiple disciplines [...
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Chapter
Numerical Methods for DNLS
In this section, we briefly discuss the numerical methods that have been used extensively throughout this book to obtain the numerical solutions discussed herein, as well as to analyze their linear stability a...
