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Improved Maximum Entropy Analysis with an Extended Search Space · Around

2011

Improved Maximum Entropy Analysis with an Extended Search Space

Rothkopf, Alexander

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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.

Built on

E. T. Jaynes, Prior information and ambiguity in inverse problems, in: SIAM-AMS Proceedings, McLaughlin, 151–166, URL http://bayes.wustl.edu , 1984
1984
Earlier work this paper cites.
R. Bryan, Maximum entropy analysis of oversampled data problems, European Biophysics Journal 18 (1990) 165–174, ISSN 0175-7571, URL http://dx.doi.org/10.1007/BF02427376 , 10.1007/BF02427376
1990
Earlier work this paper cites.
M. Jarrell, J. Gubernatis, Bayesian inference and the analytic continuation of imaginary-time quantum Monte Carlo data, Physics Reports 269 (3) (1996) 133–195, ISSN 0370-1573, doi: 10.1016/0370-1573(95)00074-7 , URL http://www.sciencedirect.com/science/article/pii/037015739500%0747
1996
Earlier work this paper cites.

Similar

M. Asakawa, T. Hatsuda, Y. Nakahara, Maximum entropy analysis of the spectral functions in lattice QCD, Prog.Part.Nucl.Phys. 46 (2001) 459–508, doi: 10.1016/S0146-6410(01)00150-8
2001
Cited alongside, same era.
D. Nickel, Extraction of Spectral Functions from Dyson-Schwinger Studies via the Maximum Entropy Method, Annals Phys. 322 (2007) 1949–1960, doi: 10.1016/j.aop.2006.09.002
2006
Cited alongside, same era.

Then

A. Rothkopf, ExtMEM (Maximum Entropy Method with an extended search space), URL http://www.scicode.org/ExtMEM , source code and manual available at http://www.scicode.org/ExtMEM, 2011
2011
Closest in time.
A. Rothkopf, T. Hatsuda, S. Sasaki, Complex Heavy-Quark Potential at Finite Temperature from Lattice QCD, Phys.Rev.Lett. 108 (2012) 162001
2012
Closest in time.

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