Regensburg 2025 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 22: Poster: Statistical Physics

DY 22.1: Poster

Wednesday, March 19, 2025, 10:00–12:00, P3

Adaptive Quasi-Monte Carlo Quadrature for Concentrated Distributions in Bayesian Inference — •Jinyi Zhou and Sebastian Matera — Fritz-Haber-Institut der MPG, Berlin

By its probabilistic formulation, Bayesian inference cures many of the problems of the traditional parameter-fitting approach, such as potential ill-posedness and the lack of reliable uncertainty estimates. However, for highly nonlinear and sensitive models, the Bayesian posterior distribution can become complex and is often concentrated in a small fraction of the parameter space. This challenges established sampling approaches, which typically perform well only for smooth distributions. We address this challenge with a novel adaptive Quasi-Monte Carlo (aQMC) quadrature method. This approach combines the highly uniform coverage of Quasi-Monte Carlo with a greedy iterative subdivision algorithm, concentrating the sampling in subdomains where the quadrature error is expected to be largest. In addition to testing on benchmark functions, we demonstrate our approach on a kinetic model from the field of catalysis. In this field, concentrated distributions are expected because, even with the best priors derived from quantum chemical calculations, uncertainties can span several orders of magnitude for the predicted catalytic response, whereas experimental data is highly accurate in comparison.

Keywords: Numerical integration; Quasi-Monte Carlo; Bayesian inference; Chemical kinetics; Parameter estimation