My PhD student Edoardo Bandoni, along with Julien Stoehr and myself, completed a paper on validating (Bayesian) kernel quadrature with unbounded domains of integration. Which connects with probabilistic numerics, since the integrand is modelled as a Gaussian process. And RKHS methods. As opposed to Monte Carlo estimators, quadrature methods approximate integrals of smooth functions with worst-case error decaying at a minimax rate α/d for smoothness α in dimension d. Existing rate-optimal quadrature methods often depend on deterministic point sets tailored to a specific kernel, making them sensitive to misspecification and thus less robust in practice. This paper studies instead randomised quadrature methods, with a focus on robustness rather than on kernel-specific optimality. We construct an explicit, n-dependent, sampling distribution that achieves minimax rates for worst-case errors over smoothness classes without requiring knowledge of the kernel. This kernel-agnostic design does improve robustness while retaining optimal rates and extends Briol et al. (2019) to the unbounded case. Which cannot always be easily handled by a change of variables. Our result thus mostly covers unbounded sampling measures such as Gaussian and Student-t distributions, extending beyond compact domains. The results provide both theoretical guarantees and a practical recipe for robust, rate-optimal, randomised quadrature. [The above is mostly stated in the abstract.]
Archive for uncertainty quantification
optimal sampling for kernel quadrature on unbounded domains
Posted in Books, Statistics, University life with tags Bayesian quadrature, bois de Boulogne, contraction rate, ERC Synergy Grant, Gaussian processes, minimaxity, Monte Carlo integration, numerical integration, Ocean, probabilistic integration, probabilistic numerics, RKHS, sunset, uncertainty quantification, Université Paris Dauphine on May 22, 2026 by xi'andi ritorno a Venezia, nella privacy oceanica
Posted in pictures, Running, Statistics, Travel, University life with tags #ERCSyG, Bayesian privacy, Campo Sant'Alviso, canals, differential privacy, ERC, ERC Synergy Grant, Italia, laguna, Les Houches, Ocean, San Giobbe, swimming pool, uncertainty quantification, Università Ca' Foscari Venezia, Venezia, visiting position, workshop on March 15, 2026 by xi'an
persuasive (and Oceanic) privacy
Posted in Books, Mountains, pictures, Statistics, Travel, University life with tags #ERCSyG, adversarial strategy, arXiv, Bayesian decision theory, Bayesian privacy, decision-making agents, differential privacy, ERC, ERC Synergy Grant, fairness, French Alps, game theory, Les Houches, Ocean, uncertainty quantification, Università Ca' Foscari Venezia, Université Paris Dauphine, Venice, workshop on February 3, 2026 by xi'an
I am quite excited about the paper James Baillie, Joshua Bon, Judith Rousseau, and myself just arXived! A novel framework for measuring privacy we have been working on for at least the past year, partly through the previous Les Houches privacy workshops. In the spirit of these workshops and the larger scale ERC Synergy grant OCEAN, we develop therein a rather generic Bayesian game-theoretic perspective on achieving statistical privacy. It involves a Sender (observing the original data and delivering a limited output) and a Receiver (with potential adversarial intentions). The paper mostly focus on setting a theoretical framework, including the creation of new, purpose-driven privacy definitions that are rigorously justified, while also allowing for the assessment of existing privacy guarantees through game theory. While this was not our original intent, we show that pure and probabilistic differential privacy notions, in the Dwork et al. (2006) sense, are special cases of our framework. This setting provides new interpretations of the post-processing inequality. Furthermore, and somewhat more importantly, we also prove that our privacy guarantees can be established for deterministic algorithms, which are outside current privacy standards. Hopefully, we’ll make further progress at the incoming privacy workshop next month, to be held in Venice (again).
ERC postdoc position on scalable experimental design, in Oxford, UK
Posted in Statistics, Travel, University life with tags Bayesian deep learning, Britain, data-driven algorithms, ERC, ERC Starting Grant, European Research Council, experimental design, Horizon Europe, LLM, machine learning, postdoctoral position, scalable MCMC, simulation-based inference, UK, UKRI, uncertainty quantification, University of Oxford on August 8, 2025 by xi'an
[fool’s] gold standard science
Posted in Books, pictures, Travel, University life with tags @ScientistTrump, Bretton Woods, Donald Trump, Executive Order, falsification, gold standard, Karl Popper, misspecified model, Newspeak, polygraph, Stand up for Science, Stand Up To Trump, The New York Times, Trump administration, uncertainty quantification, White House on June 11, 2025 by xi'an
In this new presidential order of 23 May 2025, Trump pretends to
“restore the scientific integrity policies of my first Administration and ensures that agencies practice data transparency, acknowledge relevant scientific uncertainties, are transparent about the assumptions and likelihood of scenarios used, approach scientific findings objectively, and communicate scientific data accurately”
repeating his goal in
“restoring a gold standard for science to ensure that federally funded research is transparent, rigorous, and impactful, and that Federal decisions are informed by the most credible, reliable, and impartial scientific evidence available”
where
““Weight of scientific evidence” means an approach to scientific evaluation in which each piece of relevant information is considered based on its quality and relevance, and then transparently integrated with other relevant information to inform the scientific evaluation prior to making a judgment about the scientific evaluation. Quality and relevance determinations, at a minimum, should include consideration of study design, fitness for purpose, replicability, peer review, and transparency and reliability of data.”
While the order that
“science [in a federal agency should be] conducted in a manner that is:
(i) reproducible;
(ii) transparent;
(iii) communicative of error and uncertainty;
(iv) collaborative and interdisciplinary;
(v) skeptical of its findings and assumptions;
(vi) structured for falsifiability of hypotheses;
(vii) subject to unbiased peer review;
(viii) accepting of negative results as positive outcomes; and
(ix) without conflicts of interest”
sounds nice and dandy, incl. even a Popperian item!—while I highly doubt the Agent Orange has ever read anything from the author of Open society and its enemies—as well as an assessment of uncertainty and a critical look at the role of models—as if we were not, as a whole, following or trying to follow these tenets!—, the true intent of this order is to submit all research produced by federal agents and federally funded researchers to a vetting by political appointees before submission to a (vetted) scientific journal. As already been put into practice in some Departments. The rosy terms that set how science should be done are turned tupsy-turvy to the Trump administration Newspeak, while the purges in said administration render quality control more illusory than ever… Even the use of the term Gold Standard in a US policy declaration shows how little Trump understands about the term, given the USA abandoned at least twice the gold standard, in 1933 and 1978.
A few days after I wrote this piece, the New York Times published an article pointing out the above (in better terms) and reporting on an open letter from Stand Up for Science signalling the dreadful consequences of the executive order. With a primary correction to the above picture. And the central message that
We view this Executive Order as an escalation of the ongoing assault on science. The first six sections employ common scientific language to spell out a “gold standard” for science that would not strengthen science, but instead would introduce stifling limits on intellectual freedom in our Nation’s laboratories and federal funding agencies. Notably, the order comes from an administration that has already defunded areas of research they do not agree with, pushed vaccine misinformation despite widespread evidence, lied about the impacts of climate change, and incorrectly defined sex determination as binary, when biology proves it is not, in their own Executive Order. Throughout the document, scientific language is hijacked, and ideas are turned on their heads.
And then Andrew decided to discuss its ridiculness on 03 June and again on 03 June. (Which made me realize polygraphs are still used by US law enforcement agencies!)
