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@ARTICLE{Xiao:903180,
      author       = {Xiao, Sinan and Xu, Teng and Reuschen, Sebastian and Nowak,
                      Wolfgang and Hendricks Franssen, Harrie-Jan},
      title        = {{B}ayesian {I}nversion of {M}ulti‐{G}aussian
                      {L}og‐{C}onductivity {F}ields {W}ith {U}ncertain
                      {H}yperparameters: {A}n {E}xtension of {P}reconditioned
                      {C}rank‐{N}icolson {M}arkov {C}hain {M}onte {C}arlo {W}ith
                      {P}arallel {T}empering},
      journal      = {Water resources research},
      volume       = {57},
      number       = {9},
      issn         = {0043-1397},
      address      = {[New York]},
      publisher    = {Wiley},
      reportid     = {FZJ-2021-04900},
      pages        = {e2021WR030313},
      year         = {2021},
      abstract     = {In conventional Bayesian geostatistical inversion, specific
                      values of hyperparameters characterizing the prior
                      distribution of random fields are required. However, these
                      hyperparameters are typically very uncertain in practice.
                      Thus, it is more appropriate to consider the uncertainty of
                      hyperparameters as well. The preconditioned Crank-Nicolson
                      Markov chain Monte Carlo with parallel tempering (pCN-PT)
                      has been used to efficiently solve the conventional Bayesian
                      inversion of high-dimensional multi-Gaussian random fields.
                      In this study, we extend pCN-PT to Bayesian inversion with
                      uncertain hyperparameters of multi-Gaussian fields. To
                      utilize the dimension robustness of the preconditioned
                      Crank-Nicolson algorithm, we reconstruct the problem by
                      decomposing the random field into hyperparameters and white
                      noise. Then, we apply pCN-PT with a Gibbs split to this
                      “new” problem to obtain the posterior samples of
                      hyperparameters and white noise, and further recover the
                      posterior samples of spatially distributed model parameters.
                      Finally, we apply the extended pCN-PT method for estimating
                      a finely resolved multi-Gaussian log-hydraulic conductivity
                      field from direct data and from head data to show its
                      effectiveness. Results indicate that the estimation of
                      hyperparameters with hydraulic head data is very challenging
                      and the posterior distributions of hyperparameters are only
                      slightly narrower than the prior distributions. Direct
                      measurements of hydraulic conductivity are needed to narrow
                      more the posterior distribution of hyperparameters. To the
                      best of our knowledge, this is a first accurate and fully
                      linearization free solution to Bayesian multi-Gaussian
                      geostatistical inversion with uncertain hyperparameters.},
      cin          = {IBG-3},
      ddc          = {550},
      cid          = {I:(DE-Juel1)IBG-3-20101118},
      pnm          = {2173 - Agro-biogeosystems: controls, feedbacks and impact
                      (POF4-217) / DFG project 359880532 - Computergestützter
                      Ansatz zur Kalibrierung und Validierung mathematischer
                      Modelle für Strömungen im Untergrund - COMPU-FLOW},
      pid          = {G:(DE-HGF)POF4-2173 / G:(GEPRIS)359880532},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000703704400032},
      doi          = {10.1029/2021WR030313},
      url          = {https://juser.fz-juelich.de/record/903180},
}