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@ARTICLE{Xu:890096,
      author       = {Xu, Teng and Reuschen, Sebastian and Nowak, Wolfgang and
                      Hendricks Franssen, Harrie‐Jan},
      title        = {{P}reconditioned {C}rank‐{N}icolson {M}arkov {C}hain
                      {M}onte {C}arlo {C}oupled {W}ith {P}arallel {T}empering:
                      {A}n {E}fficient {M}ethod for {B}ayesian {I}nversion of
                      {M}ulti‐{G}aussian {L}og‐{H}ydraulic {C}onductivity
                      {F}ields},
      journal      = {Water resources research},
      volume       = {56},
      number       = {8},
      issn         = {1944-7973},
      address      = {[New York]},
      publisher    = {Wiley},
      reportid     = {FZJ-2021-00685},
      pages        = {1-19},
      year         = {2020},
      note         = {Kein Post-print verfügbar},
      abstract     = {Geostatistical inversion with quantified uncertainty for
                      nonlinear problems requires techniques for providing
                      conditional realizations of the random field of interest.
                      Many first‐order second‐moment methods are being
                      developed in this field, yet almost impossible to critically
                      test them against high‐accuracy reference solutions in
                      high‐dimensional and nonlinear problems. Our goal is to
                      provide a high‐accuracy reference solution algorithm.
                      Preconditioned Crank‐Nicolson Markov chain Monte Carlo
                      (pCN‐MCMC) has been proven to be more efficient in the
                      inversion of multi‐Gaussian random fields than traditional
                      MCMC methods; however, it still has to take a long chain to
                      converge to the stationary target distribution. Parallel
                      tempering aims to sample by communicating between multiple
                      parallel Markov chains at different temperatures. In this
                      paper, we develop a new algorithm called pCN‐PT. It
                      combines the parallel tempering technique with pCN‐MCMC to
                      make the sampling more efficient, and hence converge to a
                      stationary distribution faster. To demonstrate the
                      high‐accuracy reference character, we test the accuracy
                      and efficiency of pCN‐PT for estimating a multi‐Gaussian
                      log‐hydraulic conductivity field with a relative high
                      variance in three different problems: (1) in a
                      high‐dimensional, linear problem; (2) in a
                      high‐dimensional, nonlinear problem and with only few
                      measurements; and (3) in a high‐dimensional, nonlinear
                      problem with sufficient measurements. This allows testing
                      against (1) analytical solutions (kriging), (2) rejection
                      sampling, and (3) pCN‐MCMC in multiple, independent runs,
                      respectively. The results demonstrate that pCN‐PT is an
                      asymptotically exact conditional sampler and is more
                      efficient than pCN‐MCMC in geostatistical inversion
                      problems.},
      cin          = {IBG-3},
      ddc          = {550},
      cid          = {I:(DE-Juel1)IBG-3-20101118},
      pnm          = {255 - Terrestrial Systems: From Observation to Prediction
                      (POF3-255) / DFG project 359880532 - Computergestützter
                      Ansatz zur Kalibrierung und Validierung mathematischer
                      Modelle für Strömungen im Untergrund - COMPU-FLOW},
      pid          = {G:(DE-HGF)POF3-255 / G:(GEPRIS)359880532},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000582701700068},
      doi          = {10.1029/2020WR027110},
      url          = {https://juser.fz-juelich.de/record/890096},
}