Bayesian probabilistic numerical methods

“…in isolation, the error of a numerical method can often be studied and understood, but when composed into a pipeline the resulting error structure maybe non-trivial and its analysis becomes more difficult. The real power of probabilistic numerics lies in its application to pipelines of numerical methods, where the probabilistic formulation permits analysis of variance (ANOVA) to understand the contribution of each discretisation to the overall numerical error.”

Jon Cockayne (Warwick), Chris Oates (formerly Warwick), T.J. Sullivan, and Mark Girolami (formerly Warwick) got their survey on Bayesian probabilistic numerical methods in the SIAM (Society for Industrial and Applied Mathematics) Review, which is quite a feat given the non-statistical flavour of the journal (although Art Owen is now one of the editors of the review). As already reported in some posts on the ‘Og, the concept relies on the construction of a prior measure over a set of potential solutions, and numerical methods are assessed against the associated posterior measure. Not only is this framework more compelling in a conceptual sense, but it also leads to novel probabilistic numerical methods managing to solve quite challenging numerical tasks. Congrats to the authors!

Error and Inference [arXived]

Following my never-ending series of posts on the book Error and Inference, (edited) by Deborah Mayo and Ari Spanos (and kindly sent to me by Deborah), I decided to edit those posts into a (slightly) more coherent document, now posted on arXiv. And to submit it as a book review to Siam Review, even though I had not high expectations it fits the purpose of the journal: the review was rejected between the submission to arXiv and the publication of this post!