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08/08/2022
Statistical Properties of the Probabilistic Numeric Linear Solver BayesCG
We analyse the calibration of BayesCG under the Krylov prior, a probabil...
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11/15/2021
Theoretical Guarantees for the Statistical Finite Element Method
The statistical finite element method (StatFEM) is an emerging probabili...
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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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02/01/2021
A Probabilistic Taylor Expansion with Applications in Filtering and Differential Equations
We study a class of Gaussian processes for which the posterior mean, for...
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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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12/23/2020
Probabilistic Iterative Methods for Linear Systems
This paper presents a probabilistic perspective on iterative methods for...
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09/03/2020
Probabilistic Gradients for Fast Calibration of Differential Equation Models
Calibration of large-scale differential equation models to observational...
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08/07/2020
A Probabilistic Numerical Extension of the Conjugate Gradient Method
We present a Conjugate Gradient (CG) implementation of the probabilistic...
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05/08/2020
Optimal Thinning of MCMC Output
The use of heuristics to assess the convergence and compress the output ...
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06/24/2019
A Role for Symmetry in the Bayesian Solution of Differential Equations
The interpretation of numerical methods, such as finite difference metho...
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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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10/08/2018
Probabilistic Linear Solvers: A Unifying View
Several recent works have developed a new, probabilistic interpretation ...
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05/18/2018
On the Bayesian Solution of Differential Equations
The interpretation of numerical methods, such as finite difference metho...
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01/16/2018
A Bayesian Conjugate Gradient Method
A fundamental task in numerical computation is the solution of large lin...
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06/11/2017
On the Sampling Problem for Kernel Quadrature
The standard Kernel Quadrature method for numerical integration with ran...
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02/13/2017
Bayesian Probabilistic Numerical Methods
The emergent field of probabilistic numerics has thus far lacked clear s...
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01/15/2017