Stein's method compares probability distributions through the study of a class of linear
operators called Stein operators. While mainly studied in probability and used to underpin …

Markov chain Monte Carlo is the engine of modern Bayesian statistics, being used to
approximate the posterior and derived quantities of interest. Despite this, the issue of how …

The use of heuristics to assess the convergence and compress the output of Markov chain
Monte Carlo can be sub-optimal in terms of the empirical approximations that are produced …

This paper proposes and studies a numerical method for approximation of posterior
expectations based on interpolation with a Stein reproducing kernel. Finite-sample-size …

This PhD thesis combines two of the most exciting research areas of the last decades:
quantum computing and machine learning. We introduce dissipative quantum neural …

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 …

For two decades, reproducing kernels and their associated discrepancies have facilitated
elegant theoretical analyses in the setting of quasi Monte Carlo. These same tools are now …

We analyse the performance of several iterative algorithms for the quantisation of a
probability measure μ, based on the minimisation of a Maximum Mean Discrepancy (MMD) …

Unbiased assessment of the predictivity of models learnt by supervised machine learning
(ML) methods requires knowledge of the learned function over a reserved test set (not used …

Due to the growing adoption of deep neural networks in many fields of science and
engineering, modeling and estimating their uncertainties has become of primary importance …