
Bayesian Numerical Methods for Nonlinear Partial Differential Equations
The numerical solution of differential equations can be formulated as an...
read it

A Probabilistic Taylor Expansion with Applications in Filtering and Differential Equations
We study a class of Gaussian processes for which the posterior mean, for...
read it

Testing whether a Learning Procedure is Calibrated
A learning procedure takes as input a dataset and performs inference for...
read it

Probabilistic Iterative Methods for Linear Systems
This paper presents a probabilistic perspective on iterative methods for...
read it

Probabilistic Gradients for Fast Calibration of Differential Equation Models
Calibration of largescale differential equation models to observational...
read it

A Probabilistic Numerical Extension of the Conjugate Gradient Method
We present a Conjugate Gradient (CG) implementation of the probabilistic...
read it

Optimal Thinning of MCMC Output
The use of heuristics to assess the convergence and compress the output ...
read it

A Role for Symmetry in the Bayesian Solution of Differential Equations
The interpretation of numerical methods, such as finite difference metho...
read it

Optimality Criteria for Probabilistic Numerical Methods
It is well understood that Bayesian decision theory and average case ana...
read it

Probabilistic Linear Solvers: A Unifying View
Several recent works have developed a new, probabilistic interpretation ...
read it

On the Bayesian Solution of Differential Equations
The interpretation of numerical methods, such as finite difference metho...
read it

A Bayesian Conjugate Gradient Method
A fundamental task in numerical computation is the solution of large lin...
read it

On the Sampling Problem for Kernel Quadrature
The standard Kernel Quadrature method for numerical integration with ran...
read it

Bayesian Probabilistic Numerical Methods
The emergent field of probabilistic numerics has thus far lacked clear s...
read it

Probabilistic Numerical Methods for PDEconstrained Bayesian Inverse Problems
This paper develops meshless methods for probabilistically describing di...
read it
Jon Cockayne
is this you? claim profile