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@ARTICLE{Rings:21347,
      author       = {Rings, J. and Vrugt, J.A. and Schoups, G. and Huisman, J.A.
                      and Vereecken, H.},
      title        = {{B}ayesian model averaging using particle filtering and
                      {G}aussian mixture modeling: {T}heory, concepts, and
                      simulation experiments},
      journal      = {Water resources research},
      volume       = {48},
      issn         = {0043-1397},
      address      = {Washington, DC},
      publisher    = {AGU},
      reportid     = {PreJuSER-21347},
      pages        = {W05520},
      year         = {2012},
      note         = {Jasper A. Vrugt would like to acknowledge financial support
                      from the LDRD project "Multilevel Adaptive Sampling for
                      Multiscale Inverse Problems'' of the Los Alamos National
                      Laboratory.},
      abstract     = {Bayesian model averaging (BMA) is a standard method for
                      combining predictive distributions from different models. In
                      recent years, this method has enjoyed widespread application
                      and use in many fields of study to improve the spread-skill
                      relationship of forecast ensembles. The BMA predictive
                      probability density function (pdf) of any quantity of
                      interest is a weighted average of pdfs centered around the
                      individual (possibly bias-corrected) forecasts, where the
                      weights are equal to posterior probabilities of the models
                      generating the forecasts, and reflect the individual models
                      skill over a training (calibration) period. The original BMA
                      approach presented by Raftery et al. (2005) assumes that the
                      conditional pdf of each individual model is adequately
                      described with a rather standard Gaussian or Gamma
                      statistical distribution, possibly with a heteroscedastic
                      variance. Here we analyze the advantages of using BMA with a
                      flexible representation of the conditional pdf. A joint
                      particle filtering and Gaussian mixture modeling framework
                      is presented to derive analytically, as closely and
                      consistently as possible, the evolving forecast density
                      (conditional pdf) of each constituent ensemble member. The
                      median forecasts and evolving conditional pdfs of the
                      constituent models are subsequently combined using BMA to
                      derive one overall predictive distribution. This paper
                      introduces the theory and concepts of this new ensemble
                      postprocessing method, and demonstrates its usefulness and
                      applicability by numerical simulation of the rainfall-runoff
                      transformation using discharge data from three different
                      catchments in the contiguous United States. The revised BMA
                      method receives significantly lower-prediction errors than
                      the original default BMA method (due to filtering) with
                      predictive uncertainty intervals that are substantially
                      smaller but still statistically coherent (due to the use of
                      a time-variant conditional pdf).},
      keywords     = {J (WoSType)},
      cin          = {IBG-3},
      ddc          = {550},
      cid          = {I:(DE-Juel1)IBG-3-20101118},
      pnm          = {Terrestrische Umwelt},
      pid          = {G:(DE-Juel1)FUEK407},
      shelfmark    = {Environmental Sciences / Limnology / Water Resources},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000304253000002},
      doi          = {10.1029/2011WR011607},
      url          = {https://juser.fz-juelich.de/record/21347},
}