Applying recursive numerical integration techniques for solving high dimensional integrals

@article{Ammon2016ApplyingRN,
title={Applying recursive numerical integration techniques for solving high dimensional integrals},
author={A. Ammon and A. Genz and T. Hartung and K. Jansen and H. Leovey and J. Volmer},
journal={arXiv: High Energy Physics - Lattice},
year={2016}
}

The error scaling for Markov-Chain Monte Carlo techniques (MCMC) with $N$ samples behaves like $1/\sqrt{N}$. This scaling makes it often very time intensive to reduce the error of computed observables, in particular for applications in lattice QCD. [...] Key Method The basic idea of this method is to use an efficient low-dimensional quadrature rule (usually of Gaussian type) and apply it iteratively to integrate over high-dimensional observables and Boltzmann weights.Expand

In lattice field theory, the interactions of elementary particles can be computed via high-dimensional integrals. Markov-chain Monte Carlo (MCMC) methods based on importance sampling are normally… Expand

Division and label structured population models (DLSPMs) are a class of partial differential equations (PDEs) that have been used to study intracellular dynamics in dividing cells. DLSPMs have… Expand

Statistical packages have been used for decades to analyze large datasets or to perform mathematically intractable statistical methods. These packages are not capable of working with random variables… Expand