A new Bayesian approach to the reconstruction of spectral functions

Burnier, Yannis; Rothkopf, Alexander Karl (20 November 2014). A new Bayesian approach to the reconstruction of spectral functions. PoS - proceedings of science, LATTICE2013(490). Scuola Internazionale Superiore di Studi Avanzati SISSA

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We present a novel approach for the reconstruction of spectra from Euclidean correlator data that makes close contact to modern Bayesian concepts. It is based upon an axiomatically justified dimensionless prior distribution, which in the case of constant prior function m(ω) only imprints smoothness on the reconstructed spectrum. In addition we are able to analytically integrate out the only relevant overall hyper-parameter α in the prior, removing the necessity for Gaussian approximations found e.g. in the Maximum Entropy Method. Using a quasi-Newton minimizer and high-precision arithmetic, we are then able to find the unique global extremum of P[ρ|D] in the full Nω » Nτ dimensional search space. The method actually yields gradually improving reconstruction results if the quality of the supplied input data increases, without introducing artificial peak structures, often encountered in the MEM. To support these statements we present mock data analyses for the case of zero width delta peaks and more realistic scenarios, based on the perturbative Euclidean Wilson Loop as well as the Wilson Line correlator in Coulomb gauge.

Item Type:

Conference or Workshop Item (Paper)

Division/Institute:

10 Strategic Research Centers > Albert Einstein Center for Fundamental Physics (AEC)
08 Faculty of Science > Institute of Theoretical Physics

UniBE Contributor:

Burnier, Yannis and Rothkopf, Alexander Karl

Subjects:

500 Science > 530 Physics

ISSN:

1824-8039

Publisher:

Scuola Internazionale Superiore di Studi Avanzati SISSA

Language:

English

Submitter:

Esther Fiechter

Date Deposited:

02 Dec 2014 14:18

Last Modified:

06 Dec 2014 07:46

BORIS DOI:

10.7892/boris.60606

URI:

https://boris.unibe.ch/id/eprint/60606

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