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@PHDTHESIS{Ghanem:840299,
      author       = {Ghanem, Khaldoon},
      title        = {{S}tochastic {A}nalytic {C}ontinuation: {A} {B}ayesian
                      {A}pproach},
      school       = {RWTH Aachen University},
      type         = {Dissertation},
      reportid     = {FZJ-2017-07845},
      pages        = {183 p.},
      year         = {2017},
      note         = {Dissertation, RWTH Aachen University, 2017},
      abstract     = {The 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.},
      cin          = {JSC},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {511 - Computational Science and Mathematical Methods
                      (POF3-511) / AICES Aachen Institute for Advanced Study in
                      Computational Engineering Science (AICES-AACHEN-20170406)},
      pid          = {G:(DE-HGF)POF3-511 / G:(DE-Juel1)AICES-AACHEN-20170406},
      typ          = {PUB:(DE-HGF)11},
      url          = {https://juser.fz-juelich.de/record/840299},
}