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SIAM Conference on Uncertainty Quantification (UQ20)

Tuesday – 24.03.2020

10:30

iCal
Fred J. Hickernell | Illinois Institute of Technology | United States

Alexandra Gessner | University of Tuebingen | Germany

MS161: Probabilistic Numerical Methods for Cubature

Room:
MW HS 0350

Topic:
Probability Theory for UQ

Form of presentation:
Mini-symposium

Duration:
120 Minutes

The central tenet of probabilistic numerics is that uncertainty due to discretisation can be formally modelled. For numerical cubature in the presence of a limited computational budget, it is natural to seek to exploit any contextual information that may be available on the integrand. Classical cubatures, such as spline-based or Gaussian cubatures, are able to exploit abstract mathematical information such as the number of continuous derivatives of the integrand. However, in situations where information of a more contextual and perhaps speculative nature is available to the analyst, the use of generic classical cubatures can be sub-optimal by failing to take this information into account. The language of probabilities provides one mechanism in which diverse contextual information about the integrand can be captured. Through the formalism of a stochastic process model, the analyst can encode both abstract mathematical information, such as the number of continuous derivatives of the integrand, and speciﬁc contextual information, such as the possibility of a local trend or a periodic component. This minisymposium focuses on the development of probabilistic methods for numerical cubature, showcasing approaches that are state-of-the-art in this nascent research field.

10:30

The Successes and Challenges of Automatic Bayesian Cubature

11:30

Integrals of linearly constrained Gaussians