5 papers · 1 filter
Asymptotic and pre-asymptotic convergence of sparse grids for anisotropic kernel interpolation
Elliot J. Addy, Aretha L. Teckentrup
Sparse grids are popular tools for high-dimensional function approximation. In this work, we study the use of sparse grids for interpolation using separable Matérn kernels $Φ_{\b…
Lengthscale-informed sparse grids for kernel methods in high dimensions
Elliot J. Addy, Jonas Latz, Aretha L. Teckentrup
Kernel interpolation, especially in the context of Gaussian process emulation, is a widely used technique in surrogate modelling, where the goal is to cheaply approximate an input-…
Deep Gaussian Process Priors for Bayesian Image Reconstruction
Jonas Latz, Aretha L. Teckentrup, Simon Urbainczyk
In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used:…
Smoothed Circulant Embedding with Applications to Multilevel Monte Carlo Methods for PDEs with Random Coefficients
Anastasia Istratuca, Aretha Teckentrup
We consider the computational efficiency of Monte Carlo (MC) and Multilevel Monte Carlo (MLMC) methods applied to partial differential equations with random coefficients. These ari…
Posterior Consistency for Gaussian Process Approximations of Bayesian Posterior Distributions
Andrew M. Stuart, Aretha L. Teckentrup
We study the use of Gaussian process emulators to approximate the parameter-to-observation map or the negative log-likelihood in Bayesian inverse problems. We prove error bounds on…