Now in its second edition, this accessible text presents a unified Bayesian treatment of state-
of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state …

Over forty years ago average-case error was proposed in the applied mathematics literature
as an alternative criterion with which to assess numerical methods. In contrast to worst-case …

This article attempts to place the emergence of probabilistic numerics as a mathematical–
statistical research field within its historical context and to explore how its gradual …

We introduce kernel thinning, a new procedure for compressing a distribution $\mathbb {P} $
more effectively than iid sampling or standard thinning. Given a suitable reproducing kernel …

Probabilistic integration is a Bayesian inference technique for numerical integration, and has
received much attention in the community of scientific and engineering computations. The …

Likelihood-free inference methods typically make use of a distance between simulated and
real data. A common example is the maximum mean discrepancy (MMD), which has …

Despite the ubiquity of the Gaussian process regression model, few theoretical results are
available that account for the fact that parameters of the covariance kernel typically need to …

Stein discrepancies have emerged as a powerful tool for retrospective improvement of
Markov chain Monte Carlo output. However, the question of how to design Markov chains …

Parallel Gaussian Process Surrogate Bayesian Inference with Noisy Likelihood Evaluations
Page 1 Bayesian Analysis (2021) 16, Number 1, pp. 147–178 Parallel Gaussian Process …

We study kernel quadrature rules with convex weights. Our approach combines the spectral
properties of the kernel with recombination results about point measures. This results in …