Improved Maximum Entropy Analysis with an Extended Search Space
arXiv:1110.6285 · doi:10.1016/j.jcp.2012.12.023
Abstract
The standard implementation of the Maximum Entropy Method (MEM) follows Bryan and deploys a Singular Value Decomposition (SVD) to limit the dimensionality of the underlying solution space apriori. Here we present arguments based on the shape of the SVD basis functions and numerical evidence from a mock data analysis, which show that the correct Bayesian solution is not in general recovered with this approach. As a remedy we propose to extend the search basis systematically, which will eventually recover the full solution space and the correct solution. In order to adequately approach problems where an exponentially damped kernel is used, we provide an open-source implementation, using the C/C++ language that utilizes high precision arithmetic adjustable at run-time. The LBFGS algorithm is included in the code in order to attack problems without the need to resort to a particular search space restriction.
18 pages, 6 figures, v3 includes several changes in text and figures, t.b.p. in Journal of Computational Physics, source code at http://www.scicode.org/ExtMEM
References in corpus (2)
Cited by in corpus (33)
- Heavy-flavour and quarkonium production in the LHC era: from proton-proton to heavy-ion collisions
- A novel Bayesian approach to spectral function reconstruction
- Heavy Quarkonium in Extreme Conditions
- Static quark-antiquark potential in the quark-gluon plasma from lattice QCD
- Reconstructing parton distribution functions from Ioffe time data: from Bayesian methods to Neural Networks
- Heavy-flavor production and medium properties in high-energy nuclear collisions - What next?
- Quarkonium at finite temperature: Towards realistic phenomenology from first principles
- Melting of P wave bottomonium states in the quark-gluon plasma from lattice NRQCD
- Towards the nucleon hadronic tensor from lattice QCD
- Complex heavy-quark potential and Debye mass in a gluonic medium from lattice QCD
- Charmonium spectral functions from 2+1 flavour lattice QCD
- Electrical conductivity of the quark-gluon plasma: perspective from lattice QCD
- Quarkonium in-medium properties from realistic lattice NRQCD
- Bayesian analysis of quark spectral properties from the Dyson-Schwinger equation
- Thermodynamics of strong-interaction matter from Lattice QCD
- A hard thermal loop benchmark for the extraction of the nonperturbative potential
- Bayesian study of relativistic open and hidden charm in anisotropic lattice QCD
- Rethinking the ill-posedness of the spectral function reconstruction -- why is it fundamentally hard and how Artificial Neural Networks can help
- Bayesian inference of non-positive spectral functions in quantum field theory
- Lattice QCD Thermodynamics with Physical Quark Masses
- Apparent convergence of Padé approximants for the crossover line in finite density QCD
- In-medium P-wave quarkonium from the complex lattice QCD potential
- From Complex to Stochastic Potential: Heavy Quarkonia in the Quark-Gluon Plasma
- Bayesian inference of real-time dynamics from lattice QCD
- Bryan's Maximum Entropy Method -- diagnosis of a flawed argument and its remedy
- Dual formulation of the maximum entropy method applied to analytic continuation of quantum Monte Carlo data
- INFN What Next: Ultra-relativistic Heavy-Ion Collisions
- Thermal D mesons from anisotropic lattice QCD
- Quark-Gluon Plasma: from lattice simulations to experimental results
- In-medium heavy-quarkonium from lattice QCD spectral functions
- Benchmarking the Bayesian reconstruction of the non-perturbative heavy potential
- Bottomonium in the plasma: lattice results
- The noiseless limit and improved-prior limit of the maximum entropy method and their implications for the analytic continuation problem