François-Xavier Briol

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A research frontier has emerged in scientific computation, founded on the principle that numerical error entails epistemic uncertainty that ought to be subjected to statistical analysis. This viewpoint raises several interesting challenges, including the design of statistical methods that enable the coherent propagation of probabilities through a (possibly(More)
There is renewed interest in formulating integration as a statistical inference problem , motivated by obtaining a full distribution over numerical error that can be propagated through subsequent computation. Current methods, such as Bayesian Quadrature, demonstrate impressive empirical performance but lack theoretical analysis. An important challenge is(More)
Probabilistic numerical methods aim to model numerical error as a source of epistemic uncertainty that is subject to probabilistic analysis and reasoning, enabling the principled propagation of numerical uncertainty through a computational pipeline. In this paper we focus on numerical methods for integration. We present probabilistic (Bayesian) versions of(More)
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