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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...

0 Ilja Klebanov, et al. ∙

∙ 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...

0 Ilja Klebanov, et al. ∙

∙ 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...

0 Tadashi Matsumoto, et al. ∙

∙ 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...

0 Mattes Mollenhauer, et al. ∙

∙ 11/10/2022

Error bound analysis of the stochastic parareal algorithm

Stochastic parareal (SParareal) is a probabilistic variant of the popula...

0 Kamran Pentland, et al. ∙

∙ 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...

0 Hefin Lambley, et al. ∙

∙ 01/31/2022

GParareal: A time-parallel ODE solver using Gaussian process emulation

Sequential numerical methods for integrating initial value problems (IVP...

0 Kamran Pentland, et al. ∙

∙ 12/22/2021

Dimension-independent Markov chain Monte Carlo on the sphere

We consider Bayesian analysis on high-dimensional spheres with angular c...

0 H. C. Lie, et al. ∙

∙ 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 ...

0 Birzhan Ayanbayev, et al. ∙

∙ 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...

0 Birzhan Ayanbayev, et al. ∙

∙ 04/22/2021

Bayesian Numerical Methods for Nonlinear Partial Differential Equations

The numerical solution of differential equations can be formulated as an...

0 Junyang Wang, et al. ∙

∙ 03/30/2021

Randomised one-step time integration methods for deterministic operator differential equations

Uncertainty quantification plays an important role in applications that ...

0 Han Cheng Lie, et al. ∙

∙ 12/23/2020

Testing whether a Learning Procedure is Calibrated

A learning procedure takes as input a dataset and performs inference for...

0 Jon Cockayne, et al. ∙

∙ 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...

0 M. McKerns, et al. ∙

∙ 08/27/2020

The linear conditional expectation in Hilbert space

The linear conditional expectation (LCE) provides a best linear (or rath...

0 Ilja Klebanov, et al. ∙

∙ 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...

0 L. Bonnet, et al. ∙

∙ 12/02/2019

A Rigorous Theory of Conditional Mean Embeddings

Conditional mean embeddings (CME) have proven themselves to be a powerfu...

0 Ilja Klebanov, et al. ∙

∙ 11/13/2019

Error bounds for some approximate posterior measures in Bayesian inference

In certain applications involving the solution of a Bayesian inverse pro...

0 Han Cheng Lie, et al. ∙

∙ 06/27/2019

Geodesic analysis in Kendall's shape space with epidemiological applications

We analytically determine Jacobi fields and parallel transports and comp...

0 Esfandiar Nava-Yazdani, et al. ∙

∙ 06/24/2019

Comments on the article "A Bayesian conjugate gradient method"

The recent article "A Bayesian conjugate gradient method" by Cockayne, O...

0 T. J. Sullivan, et al. ∙

∙ 01/14/2019

A Modern Retrospective on Probabilistic Numerics

This article attempts to cast the emergence of probabilistic numerics as...

0 C. J. Oates, et al. ∙

∙ 01/14/2019

Optimality Criteria for Probabilistic Numerical Methods

It is well understood that Bayesian decision theory and average case ana...

0 Chris J. Oates, et al. ∙

∙ 07/25/2018

Convergence Rates of Gaussian ODE Filters

A recently-introduced class of probabilistic (uncertainty-aware) solvers...

0 Hans Kersting, et al. ∙

∙ 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...

0 H. C. Lie, et al. ∙

∙ 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...

0 Ingmar Schuster, et al. ∙

∙ 10/16/2017

Well-posedness of Bayesian inverse problems in quasi-Banach spaces with stable priors

The Bayesian perspective on inverse problems has attracted much mathemat...

0 T. J. Sullivan, et al. ∙

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