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000840299 005__ 20210129231811.0
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000840299 037__ $$aFZJ-2017-07845
000840299 041__ $$aEnglish
000840299 1001_ $$0P:(DE-Juel1)168540$$aGhanem, Khaldoon$$b0$$eCorresponding author
000840299 245__ $$aStochastic Analytic Continuation: A Bayesian Approach$$f - 2017-06-26
000840299 260__ $$c2017
000840299 300__ $$a183 p.
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000840299 3367_ $$2BibTeX$$aPHDTHESIS
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000840299 3367_ $$0PUB:(DE-HGF)11$$2PUB:(DE-HGF)$$aDissertation / PhD Thesis$$bphd$$mphd$$s1511879854_21601
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000840299 502__ $$aDissertation, RWTH Aachen University, 2017$$bDissertation$$cRWTH Aachen University$$d2017$$o2017-06-26
000840299 520__ $$aThe stochastic sampling method (StochS) is used for the analytic continuation of quantum Monte Carlo data from the imaginary axis to the real axis. Compared to the maximum entropy method, StochS does not have explicit parameters, and one would expect the results to be unbiased. We present a very efficient algorithm for performing StochS and use it to study the effect of the discretization grid. Surprisingly, we find that the grid affects the results of StochS acting as an implicit default model. We provide a recipe for choosing a reliable StochS grid.To reduce the effect of the grid, we extend StochS into a gridless method (gStochS) by sampling the grid points from a default model instead of having them fixed. The effect of the default model is much reduced in gStochS compared to StochS and depends mainly on its width rather than its shape. The proper width can then be chosen using a simple recipe like we did in StochS.Finally, to avoid fixing the width, we go one step further and extend gStochS to sample over a whole class of default models with different widths. The extended method (eStochS) is then able to automatically relocate the grid points and concentrate them in the important region. Test cases show that eStochS gives good results resolving sharp features in the spectrum without the need for fine tuning a default model.
000840299 536__ $$0G:(DE-HGF)POF3-511$$a511 - Computational Science and Mathematical Methods (POF3-511)$$cPOF3-511$$fPOF III$$x0
000840299 536__ $$0G:(DE-Juel1)AICES-AACHEN-20170406$$aAICES Aachen Institute for Advanced Study in Computational Engineering Science (AICES-AACHEN-20170406)$$cAICES-AACHEN-20170406$$x1
000840299 8564_ $$uhttp://dx.doi.org/10.18154/RWTH-2017-06704
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