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08/19/2023
Transporting Higher-Order Quadrature Rules: Quasi-Monte Carlo Points and Sparse Grids for Mixture Distributions
Integration against, and hence sampling from, high-dimensional probabili...
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06/28/2023
A `periodic table' of modes and maximum a posteriori estimators
The last decade has seen many attempts to generalise the definition of m...
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05/05/2023
Images of Gaussian and other stochastic processes under closed, densely-defined, unbounded linear operators
Gaussian processes (GPs) are widely-used tools in spatial statistics and...
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11/16/2022
Learning linear operators: Infinite-dimensional regression as a well-behaved non-compact inverse problem
We consider the problem of learning a linear operator θ between two Hilb...
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11/10/2022
Error bound analysis of the stochastic parareal algorithm
Stochastic parareal (SParareal) is a probabilistic variant of the popula...
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09/23/2022
An order-theoretic perspective on modes and maximum a posteriori estimation in Bayesian inverse problems
It is often desirable to summarise a probability measure on a space X in...
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01/31/2022
GParareal: A time-parallel ODE solver using Gaussian process emulation
Sequential numerical methods for integrating initial value problems (IVP...
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12/22/2021
Dimension-independent Markov chain Monte Carlo on the sphere
We consider Bayesian analysis on high-dimensional spheres with angular c...
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08/10/2021
Γ-convergence of Onsager-Machlup functionals. Part II: Infinite product measures on Banach spaces
We derive Onsager-Machlup functionals for countable product measures on ...
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08/10/2021
Γ-convergence of Onsager-Machlup functionals. Part I: With applications to maximum a posteriori estimation in Bayesian inverse problems
The Bayesian solution to a statistical inverse problem can be summarised...
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04/22/2021
Bayesian Numerical Methods for Nonlinear Partial Differential Equations
The numerical solution of differential equations can be formulated as an...
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03/30/2021
Randomised one-step time integration methods for deterministic operator differential equations
Uncertainty quantification plays an important role in applications that ...
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12/23/2020
Testing whether a Learning Procedure is Calibrated
A learning procedure takes as input a dataset and performs inference for...
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09/13/2020
Optimal Bounds on Nonlinear Partial Differential Equations in Model Certification, Validation, and Experimental Design
We demonstrate that the recently developed Optimal Uncertainty Quantific...
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08/27/2020
The linear conditional expectation in Hilbert space
The linear conditional expectation (LCE) provides a best linear (or rath...
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07/10/2020
Adaptive reconstruction of imperfectly-observed monotone functions, with applications to uncertainty quantification
Motivated by the desire to numerically calculate rigorous upper and lowe...
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12/02/2019
A Rigorous Theory of Conditional Mean Embeddings
Conditional mean embeddings (CME) have proven themselves to be a powerfu...
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11/13/2019
Error bounds for some approximate posterior measures in Bayesian inference
In certain applications involving the solution of a Bayesian inverse pro...
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06/27/2019
Geodesic analysis in Kendall's shape space with epidemiological applications
We analytically determine Jacobi fields and parallel transports and comp...
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06/24/2019
Comments on the article "A Bayesian conjugate gradient method"
The recent article "A Bayesian conjugate gradient method" by Cockayne, O...
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01/14/2019
A Modern Retrospective on Probabilistic Numerics
This article attempts to cast the emergence of probabilistic numerics as...
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01/14/2019
Optimality Criteria for Probabilistic Numerical Methods
It is well understood that Bayesian decision theory and average case ana...
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07/25/2018
Convergence Rates of Gaussian ODE Filters
A recently-introduced class of probabilistic (uncertainty-aware) solvers...
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12/15/2017
Random forward models and log-likelihoods in Bayesian inverse problems
We consider the use of randomised forward models and log-likelihoods wit...
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12/07/2017
Exact active subspace Metropolis-Hastings, with applications to the Lorenz-96 system
We consider the application of active subspaces to inform a Metropolis-H...
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10/16/2017