Zobrazeno 1 - 10
of 73
pro vyhledávání: '"Cockayne, Jon"'
Gaussian processes are notorious for scaling cubically with the size of the training set, preventing application to very large regression problems. Computation-aware Gaussian processes (CAGPs) tackle this scaling issue by exploiting probabilistic lin
Externí odkaz:
http://arxiv.org/abs/2410.08796
Kalman filtering and smoothing are the foundational mechanisms for efficient inference in Gauss-Markov models. However, their time and memory complexities scale prohibitively with the size of the state space. This is particularly problematic in spati
Externí odkaz:
http://arxiv.org/abs/2405.08971
Electromagnetic radiation plays a crucial role in various physical and chemical processes. Hence, almost all astrophysical simulations require some form of radiative transfer model. Despite many innovations in radiative transfer algorithms and their
Externí odkaz:
http://arxiv.org/abs/2211.12547
We analyse the calibration of BayesCG under the Krylov prior, a probabilistic numeric extension of the Conjugate Gradient (CG) method for solving systems of linear equations with symmetric positive definite coefficient matrix. Calibration refers to t
Externí odkaz:
http://arxiv.org/abs/2208.03885
The statistical finite element method (StatFEM) is an emerging probabilistic method that allows observations of a physical system to be synthesised with the numerical solution of a PDE intended to describe it in a coherent statistical framework, to c
Externí odkaz:
http://arxiv.org/abs/2111.07691
Publikováno v:
Stat. Comput. 31(5):no. 55, 20pp., 2021
The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches can be applied. However, nonlinear partial differential equations (PDEs) pose substantial challenges from an inferential
Externí odkaz:
http://arxiv.org/abs/2104.12587
We study a class of Gaussian processes for which the posterior mean, for a particular choice of data, replicates a truncated Taylor expansion of any order. The data consist of derivative evaluations at the expansion point and the prior covariance ker
Externí odkaz:
http://arxiv.org/abs/2102.00877
A learning procedure takes as input a dataset and performs inference for the parameters $\theta$ of a model that is assumed to have given rise to the dataset. Here we consider learning procedures whose output is a probability distribution, representi
Externí odkaz:
http://arxiv.org/abs/2012.12670
This paper presents a probabilistic perspective on iterative methods for approximating the solution $\mathbf{x}_* \in \mathbb{R}^d$ of a nonsingular linear system $\mathbf{A} \mathbf{x}_* = \mathbf{b}$. In the approach a standard iterative method on
Externí odkaz:
http://arxiv.org/abs/2012.12615
Autor:
Cockayne, Jon, Duncan, Andrew B.
Calibration of large-scale differential equation models to observational or experimental data is a widespread challenge throughout applied sciences and engineering. A crucial bottleneck in state-of-the art calibration methods is the calculation of lo
Externí odkaz:
http://arxiv.org/abs/2009.04239