Bayesian quadrature for $H^1(\mu )$ with Poincaré inequality on a compact interval

Olivier Roustant, Nora Lüthen, Fabrice Gamboa

Motivated by uncertainty quantification of complex systems, we aim at finding quadrature formulas of the form ${\int }_a^{b}f(x)d\mu (x)={\sum }_{i=1}^n{w}_{i}f(x_i)$ where $f$ belongs to $…