Adaptive sampling-based quadrature rules for efficient Bayesian prediction

Quadrature Rules for Fuzzy Integrals

Efficient quadrature rules for a class of cordial Volterra integral equations: A comparative study

‎A natural algorithm with an optimal order of convergence is proposed for numerical solution of a class of cordial weakly singular Volterra integral equations‎. ‎The equations of this class appear in heat conduction problems with mixed boundary conditions‎. ‎The algorithm is based on a representation of the solution and compound Gaussian quadrature rules with graded meshes‎. ‎A comparative stud...

Doubly Adaptive Quadrature Routines based on Newton-Cote Rules

In this paper we test two recently published Matlab codes, adaptsim and adaptlob, using both a Lyness-Kaganove test and a battery type of test. Furthermore we modify these two codes using sequences of null rules in the error estimator with the intention to increase the reliability for both codes. In addition two new Matlab codes applying a locally and a globally adaptive strategy respectively a...

Sampling for Inference in Probabilistic Models with Fast Bayesian Quadrature

We propose a novel sampling framework for inference in probabilistic models: an active learning approach that converges more quickly (in wall-clock time) than Markov chain Monte Carlo (MCMC) benchmarks. The central challenge in probabilistic inference is numerical integration, to average over ensembles of models or unknown (hyper-)parameters (for example to compute the marginal likelihood or a ...

Technical Report PARG-10-01: Sampling for Bayesian Quadrature

We propose a novel form of sequential Monte Carlo integration that emerges from a decisiontheoretic treatment of approximation. Quadrature of any kind requires a set of samples of the integrand. Bayesian quadrature [O’Hagan, 1991, Rasmussen and Ghahramani, 2003] employs those samples within a Gaussian process framework to perform inference about unobserved regions of the space, and hence about ...