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 bois de Boulogne
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'an28ième semi-marathon de Boulogne Billancourt [1:28:59, 4’12″/km, 2040th, 1st M6M/76]
Posted in pictures, Running with tags bois de Boulogne, Boulogne-Billancourt, Brooks, cramp, hydratation, lease, M6M, semi de Boulogne, semi-marathon, tapas on November 18, 2025 by xi'an
Boulogne half-marathon [1:23:53, 1125/10968, 3/221 M5M, 7⁰]
Posted in Running with tags bois de Boulogne, Boulogne-Billancourt, half-marathon, Hauts de Seine, M5M, road race, Seine, semi-marathon, Université Paris Dauphine on November 21, 2024 by xi'an
murder of a Dauphine student
Posted in Kids, pictures, University life with tags bois de Boulogne, feminicide, France, minute of silence, Paris, Porte Dauphine, remembrance, students, Université Paris Dauphine on September 25, 2024 by xi'an
Masterclass in Bayesian Asymptotics, Université Paris Dauphine, 18-22 March 2024
Posted in Books, pictures, Statistics, Travel, University life with tags 2024, Bayesian asymptotics, Bayesian foundations, Bayesian inference, Bernstein-von Mises theorem, bois de Boulogne, course, empirical Bayes methods, foundation lectures, France, graduate course, IMS Lecture Notes, Judith Rousseau, marginal likelihood, MASH, Master program, masterclass, Paris, PariSanté campus, Université Paris Dauphine, University of Oxford on December 8, 2023 by xi'an
On the week of 18-22 March 2024, Judith Rousseau (Paris Dauphine & Oxford) will teach a Masterclass on Bayesian asymptotics. The masterclass takes place in Paris (on the PariSanté Campus) and consists of morning lectures and afternoon labs. Attendance is free with compulsory registration before 11 March (since the building is not accessible without prior registration).
The plan of the course is as follows
Part I: Parametric models
In this part, well- and mis-specified models will be considered.
– Asymptotic posterior distribution: asymptotic normality of the posterior, penalization induced by the prior and the Bernstein von – Mises theorem. Regular and nonregular models will be treated.
– marginal likelihood and consistency of Bayes factors/model selection approaches.
– Empirical Bayes methods: asymptotic posterior distribution for parametric empirical Bayes methods.
Part II: Nonparametric and semiparametric models
– Posterior consistency and posterior convergence rates: statistical loss functions using the theory initiated by L. Schwartz and developed by Ghosal and Van der Vaart, results on less standard or well behaved losses.
– semiparametric Bernstein von Mises theorems.
– nonparametric Bernstein von Mises theorems and Uncertainty quantification.
– Stepping away from pure Bayes approaches: generalized Bayes, one step posteriors and cut posteriors.
