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@ARTICLE{Gao:16500,
      author       = {Gao, Z. and Green, J.W. and Vanderborght, J. and Schmitt,
                      W.},
      title        = {{I}mproving {U}ncertainty {A}nalysis in {K}inetic
                      {E}valuations {U}sing {I}teratively {R}eweighted {L}east
                      {S}quares},
      journal      = {Environmental toxicology and chemistry},
      volume       = {30},
      issn         = {0730-7268},
      address      = {Lawrence, KS},
      publisher    = {SETAC [u.a.]},
      reportid     = {PreJuSER-16500},
      pages        = {2363 - 2371},
      year         = {2011},
      note         = {Record converted from VDB: 12.11.2012},
      abstract     = {Kinetic parameters of environmental fate processes are
                      usually inferred by fitting appropriate kinetic models to
                      the data using standard nonlinear least squares (NLS)
                      approaches. Although NLS is appropriate to estimate the
                      optimum parameter values, it implies restrictive assumptions
                      on data variances when the confidence limits of the
                      parameters must also be determined. Particularly in the case
                      of degradation and metabolite formation, the assumption of
                      equal error variance is often not realistic because the
                      parent data usually show higher variances than those of the
                      metabolites. Conventionally, such problems would be tackled
                      by weighted NLS regression, which requires prior knowledge
                      about the data errors. Instead of implicitly assuming equal
                      error variances or giving arbitrary weights decided by the
                      researcher, we use an iteratively reweighted least squares
                      (IRLS) algorithm to obtain the maximum likelihood estimates
                      of the model parameters and the error variances specific for
                      the different species in a model. A study with simulated
                      data shows that IRLS gives reliable results in the case of
                      both unequal and equal error variances. We also compared
                      results obtained by NLS and IRLS, with probability
                      distributions of the parameters inferred with a Markov-Chain
                      Monte-Carlo (MCMC) approach for data from aerobic
                      transformation of different chemicals in soil. Confidence
                      intervals obtained by IRLS and MCMC are consistent, whereas
                      NLS leads to very different results when the error variances
                      are distinctly different between different species. Because
                      the MCMC results can be assumed to reflect the real
                      parameter distribution imposed by the observed data, we
                      conclude that IRLS generally yields more realistic estimates
                      of confidence intervals for model parameters than NLS.},
      keywords     = {Algorithms / Confidence Intervals / Kinetics /
                      Least-Squares Analysis / Likelihood Functions / Markov
                      Chains / Models, Chemical / Monte Carlo Method / Uncertainty
                      / J (WoSType)},
      cin          = {IBG-3},
      ddc          = {690},
      cid          = {I:(DE-Juel1)IBG-3-20101118},
      pnm          = {Terrestrische Umwelt},
      pid          = {G:(DE-Juel1)FUEK407},
      shelfmark    = {Environmental Sciences / Toxicology},
      typ          = {PUB:(DE-HGF)16},
      pubmed       = {pmid:21786313},
      UT           = {WOS:000295309400024},
      doi          = {10.1002/etc.630},
      url          = {https://juser.fz-juelich.de/record/16500},
}