Testing whether a learning procedure is calibrated

J Cockayne, MM Graham, CJ Oates, TJ Sullivan… - Journal of Machine …, 2022 - jmlr.org
A learning procedure takes as input a dataset and performs inference for the parameters θ of
a model that is assumed to have given rise to the dataset. Here we consider learning …

An importance sampling approach for reliable and efficient inference in Bayesian ordinary differential equation models

J Timonen, N Siccha, B Bales, H Lähdesmäki… - Stat, 2023 - Wiley Online Library
Statistical models can involve implicitly defined quantities, such as solutions to nonlinear
ordinary differential equations (ODEs), that unavoidably need to be numerically …

Probabilistic Richardson Extrapolation

C Oates, T Karvonen, AL Teckentrup, M Strocchi… - arXiv preprint arXiv …, 2024 - arxiv.org
For over a century, extrapolation methods have provided a powerful tool to improve the
convergence order of a numerical method. However, these tools are not well-suited to …

Modelling pathwise uncertainty of Stochastic Differential Equations samplers via Probabilistic Numerics

YL Fay, S Särkkä, A Corenflos - arXiv preprint arXiv:2401.03338, 2023 - arxiv.org
Probabilistic ordinary differential equation (ODE) solvers have been introduced over the past
decade as uncertainty-aware numerical integrators. They typically proceed by assuming a …

Probabilistic solvers enable a straight-forward exploration of numerical uncertainty in neuroscience models

J Oesterle, N Krämer, P Hennig, P Berens - Journal of Computational …, 2022 - Springer
Understanding neural computation on the mechanistic level requires models of neurons and
neuronal networks. To analyze such models one typically has to solve coupled ordinary …

Uncertainty quantification for stochastic simulators with application to offshore wind farms

JC Kennedy - 2023 - theses.ncl.ac.uk
Computationally expensive computer models, known as simulators, are fundamental to the
modern scientific process. In recent years, there has been an increased interest in stochastic …