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@Article { KastnerMHMPCWHRE2023,
   title = {Compressed AFM-IR hyperspectral nanoimaging},
   journal = {Measurement Science and Technology},
   year = {2023},
   month = {9},
   day = {21},
   tags = {8.4,8.42,LargeScaleDataAna,Regression},
   state = {accepted},
   DOI = {10.1088/1361-6501/acfc27},
   author = {K{\"a}stner, B and Marschall, M and Hornemann, A and Metzner, S and Patoka, P and Cortes, S and W{\"u}bbeler, G and Hoehl, A and R{\"u}hl, E and Elster, C}
}

@Article { WubbelerMRKE2021,
   title = {Compressive nano-FTIR chemical mapping},
   journal = {Measurement Science and Technology},
   year = {2021},
   month = {12},
   day = {24},
   volume = {33},
   pages = {035402},
   tags = {8.4,8.42,LargeScaleDataAna,Regression},
   state = {accepted},
   DOI = {10.1088/1361-6501/ac407a},
   author = {W{\"u}bbeler, G and Marschall, M and R{\"u}hl, E and K{\"a}stner, B and Elster, C}
}

@Phdthesis { Metzner2021,
   title = {Bayesian data analysis for magnetic resonance fingerprinting},
   year = {2021},
   month = {12},
   day = {7},
   keywords = {publiziert},
   tags = {8.4,8.42,Messunsicherheit,Regression,Fingerprinting,LargeScaleDataAna},
   school = {TU Berlin},
   type = {PhD Thesis},
   DOI = {10.14279/depositonce-12455},
   author = {Metzner, S}
}

@Article { KlauenbergMBCvE2021,
   title = {The GUM perspective on straight-line errors-in-variables regression},
   journal = {Measurement},
   year = {2021},
   month = {11},
   day = {6},
   volume = {187},
   pages = {110340},
   tags = {8.4,8.42,Regression},
   ISSN = {0263-2241},
   DOI = {10.1016/j.measurement.2021.110340},
   author = {Klauenberg, K and Martens, S and Bošnjaković, A and Cox, M.G and van der Veen, A. M.H and Elster, C}
}

@Article { MetznerWFGKE2021,
   title = {Bayesian uncertainty quantification for magnetic resonance fingerprinting},
   journal = {Physics in Medicine \& Biology},
   year = {2021},
   month = {3},
   day = {1},
   volume = {66},
   number = {7},
   pages = {075006},
   tags = {8.4,8.42,Messunsicherheit,Regression,Fingerprinting,LargeScaleDataAna},
   DOI = {10.1088/1361-6560/abeae7},
   author = {Metzner, S and W{\"u}bbeler, G and Flassbeck, S and Gatefait, C and Kolbitsch, C and Elster, C}
}

@Article { WubbelerE2020_2,
   title = {Efficient experimental sampling through low-rank matrix recovery},
   journal = {Metrologia},
   year = {2021},
   month = {1},
   day = {7},
   volume = {58},
   number = {1},
   pages = {014002},
   note = {online},
   tags = {8.4,8.42,Regression,LargeScaleDataAna},
   state = {accepted},
   DOI = {10.1088/1681-7575/abc97b},
   author = {W{\"u}bbeler, G and Elster, C}
}

@Article { MarschallHWHRKE2020,
   title = {Compressed FTIR spectroscopy using low-rank matrix reconstruction},
   journal = {Opt. Express},
   year = {2020},
   month = {12},
   day = {10},
   volume = {26},
   number = {28},
   pages = {38762--38772},
   tags = {8.4,8.42,Regression,LargeScaleDataAna},
   DOI = {10.1364/OE.404959},
   author = {Marschall, M and Hornemann, A and W{\"u}bbeler, G and Hoehl, A and R{\"u}hl, E and K{\"a}stner, B and Elster, C}
}

@Techreport { MartensKE2020,
   title = {Calibration of a torque measuring system – GUM uncertainty evaluation for least-squares versus Bayesian inference},
   year = {2020},
   month = {11},
   day = {15},
   tags = {8.4,8.42,Regression},
   url = {http://empir.npl.co.uk/emue/wp-content/uploads/sites/49/2020/12/Compendium_M27.pdf},
   editor = {Adriaan M.H. van der Veen, Maurice G. Cox},
   address = {Teddington, United Kingdom},
   edition = {M27},
   chapter = {E14},
   booktitle = {Good Practice in Evaluating Measurement uncertainty - Compendium of examples},
   author = {Martens, S and Klauenberg, K and Elster, C}
}

@Techreport { MartensKNCEE2020,
   title = {Quantifying uncertainty when comparing measurement methods – Haemoglobin concentration as an example of correlation in straight-line regression},
   year = {2020},
   month = {11},
   day = {15},
   tags = {8.4,8.42,Regression},
   url = {http://empir.npl.co.uk/emue/wp-content/uploads/sites/49/2020/12/Compendium_M27.pdf},
   editor = {Adriaan M.H. van der Veen, Maurice G. Cox},
   address = {Teddington, United Kingdom},
   edition = {M27},
   chapter = {E13},
   booktitle = {Good Practice in Evaluating Measurement uncertainty - Compendium of examples},
   author = {Martens, S and Klauenberg, K and Neukammer, J and Cowen, S and Ellison, S L R and Elster, C}
}

@Techreport { MartensKMYFE2020,
   title = {Calibration of a sonic nozzle as an example for quantifying all uncertainties involved in straight-line regression},
   year = {2020},
   month = {11},
   day = {15},
   tags = {8.4,8.42,Regression},
   url = {http://empir.npl.co.uk/emue/wp-content/uploads/sites/49/2020/12/Compendium_M27.pdf},
   editor = {Adriaan M.H. van der Veen, Maurice G. Cox},
   address = {Teddington, United Kingdom},
   edition = {M27},
   chapter = {E11},
   booktitle = {Good Practice in Evaluating Measurement uncertainty - Compendium of examples},
   author = {Martens, S and Klauenberg, K and Mickan, B and Yardin, C and Fischer, N and Elster, C}
}

@Article { BartlEMSVW2020,
   title = {Thermal expansion and compressibility of single-crystal silicon between 285 K and 320 K},
   journal = {Measurement Science and Technology},
   year = {2020},
   month = {4},
   day = {3},
   volume = {31},
   number = {6},
   tags = {8.4,8.42,Unsicherheit,Regression},
   DOI = {10.1088/1361-6501/ab7359},
   author = {Bartl, G and Elster, C and Martin, J and Sch{\"o}del, R and Voigt, M and Walkov, A}
}

@Article { LehnertKWCSE2019,
   title = {Large-Scale Bayesian Spatial-Temporal Regression with Application to Cardiac MR-Perfusion Imaging},
   journal = {SIAM J. Imaging Sci.},
   year = {2019},
   month = {12},
   day = {12},
   volume = {12},
   number = {4},
   pages = {2035--2062},
   tags = {8.4,8.42,Regression,LargeScaleDataAna},
   DOI = {10.1137/19M1246274},
   author = {Lehnert, Judith and Kolbitsch, Christoph and W{\"u}bbeler, Gerd and Chiribiri, Amedeo and Sch{\"a}ffter, Tobias and Elster, Clemens}
}

@Article { MetznerWE2018,
   title = {Approximate large-scale Bayesian spatial modeling with application to quantitative magnetic resonance imaging},
   journal = {AStA Adv Stat Anal},
   year = {2019},
   month = {8},
   day = {29},
   volume = {103},
   number = {3},
   pages = {333--355},
   tags = {8.4,8.42,Messunsicherheit,Regression,Fingerprinting,LargeScaleDataAna},
   DOI = {10.1007/s10182-018-00334-0},
   author = {Metzner, S and W{\"u}bbeler, G and Elster, C}
}

@Article { MartinBE2019,
   title = {Application of Bayesian model averaging to the determination of thermal expansion of single-crystal silicon},
   journal = {Measurement Science and Technology},
   year = {2019},
   month = {2},
   day = {21},
   volume = {30},
   pages = {045012},
   tags = {8.4,8.42,Unsicherheit,Regression},
   DOI = {10.1088/1361-6501/ab094b},
   author = {Martin, J and Bartl, G and Elster, C}
}

@Article { LehnertWKCCESSE2018,
   title = {Pixel-wise quantification of myocardial perfusion using spatial Tikhonov regularization},
   journal = {Physics in Medicine \& Biology},
   year = {2018},
   month = {10},
   day = {10},
   volume = {63},
   pages = {215017},
   tags = {8.4, 8.42,Regression,LargeScaleDataAna},
   DOI = {10.1088/1361-6560/aae758},
   author = {Lehnert, J and W{\"u}bbeler, G and Kolbitsch, C and Chiribiri, A and Coquelin, L and Ebrard, G and Smith, N and Sch{\"a}ffter, T and Elster, C}
}

@Article { WubbelerBE2018,
   title = {Robust Bayesian linear regression with application to an analysis of the CODATA values for the Planck constant},
   journal = {Metrologia},
   year = {2018},
   month = {1},
   day = {2},
   volume = {55},
   number = {1},
   pages = {20},
   tags = {8.4,8.42,Unsicherheit,Regression},
   DOI = {10.1088/1681-7575/aa98aa},
   author = {W{\"u}bbeler, G and Bodnar, O and Elster, C}
}

@Article { ElsterW2017,
   title = {Bayesian inference using a noninformative prior for linear Gaussian random coefficient regression with inhomogeneous within-class variances},
   journal = {Comput. Stat.},
   year = {2017},
   month = {1},
   day = {3},
   volume = {32},
   number = {1},
   pages = {51--69},
   abstract = {A Bayesian inference for a linear Gaussian random coefficient regression model with inhomogeneous within-class variances is presented. The model is moti- vated by an application in metrology, but it may well find interest in other fields. We consider the selection of a noninformative prior for the Bayesian inference to address applications where the available prior knowledge is either vague or shall be ignored. The noninformative prior is derived by applying the Berger and Bernardo reference prior principle with the means of the random coefficients forming the parameters of interest. We show that the resulting posterior is proper and specify conditions for the existence of first and second moments of the marginal posterior. Simulation results are presented which suggest good frequentist properties of the proposed inference. The calibration of sonic nozzle data is considered as an application from metrology. The proposed inference is applied to these data and the results are compared to those obtained by alternative approaches.},
   keywords = {random coefficient regression, Bayesian inference, noninformative prior},
   tags = {8.42, Regression},
   DOI = {10.1007/s00180-015-0641-3},
   author = {Elster, C and W{\"u}bbeler, G}
}

@Article { DierlEFKEE2016,
   title = {Improved estimation of reflectance spectra by utilizing prior knowledge},
   journal = {Journal of the Optical Society of America A},
   year = {2016},
   month = {6},
   day = {23},
   volume = {33},
   number = {7},
   pages = {1370--1376},
   keywords = {dynamic measurement, dynamic uncertainty, deconvolution},
   tags = {8.42, Dynamik, Regression},
   DOI = {10.1364/JOSAA.33.001370},
   author = {Dierl, M and Eckhard, T and Frei, B and Klammer, M and Eichst{\"a}dt, S and Elster, C}
}

@Article { Elster2016a,
   title = {Bayesian regression versus application of least squares—an example},
   journal = {Metrologia},
   year = {2016},
   month = {1},
   day = {2},
   volume = {53},
   number = {1},
   pages = {S10},
   abstract = {Regression is an important task in metrology and least-squares methods are often applied in this context. Bayesian inference provides an alternative that can take into account available prior knowledge. We illustrate similarities and differences of the two approaches in terms of a particular nonlinear regression problem. The impact of prior knowledge utilized in the Bayesian regression depends on the amount of information contained in the data, and by considering data sets with different signal-to-noise ratios the relevance of the employed prior knowledge for the results is investigated. In addition, properties of the two approaches are explored in the context of the particular example.},
   tags = {8.4, 8.42, Unsicherheit, Regression},
   web_url = {http://stacks.iop.org/0026-1394/53/i=1/a=S10},
   DOI = {10.1088/0026-1394/53/1/S10},
   author = {Elster, C and W{\"u}bbeler, G}
}

@Article { Klauenberg2016,
   title = {Markov chain Monte Carlo methods: an introductory example},
   journal = {Metrologia},
   year = {2016},
   month = {1},
   day = {3},
   volume = {53},
   number = {1},
   pages = {S32},
   abstract = {When the Guide to the Expression of Uncertainty in Measurement (GUM) and methods from its supplements are not applicable, the Bayesian approach may be a valid and welcome alternative. Evaluating the posterior distribution, estimates or uncertainties involved in Bayesian inferences often requires numerical methods to avoid high-dimensional integrations. Markov chain Monte Carlo (MCMC) sampling is such a method---powerful, flexible and widely applied. Here, a concise introduction is given, illustrated by a simple, typical example from metrology. The Metropolis--Hastings algorithm is the most basic and yet flexible MCMC method. Its underlying concepts are explained and the algorithm is given step by step. The few lines of software code required for its implementation invite interested readers to get started. Diagnostics to evaluate the performance and common algorithmic choices are illustrated to calibrate the Metropolis--Hastings algorithm for efficiency. Routine application of MCMC algorithms may be hindered currently by the difficulty to assess the convergence of MCMC output and thus to assure the validity of results. An example points to the importance of convergence and initiates discussion about advantages as well as areas of research. Available software tools are mentioned throughout.},
   keywords = {Bayesian, MCMC, Markov chain Monte Carlo},
   tags = {8.42, Unsicherheit, Regression},
   web_url = {http://stacks.iop.org/0026-1394/53/i=1/a=S32},
   DOI = {10.1088/0026-1394/53/1/S32},
   author = {Klauenberg, K and Elster, C}
}

@Techreport { NEW04_Bayes,
   title = {A Guide to Bayesian Inference for Regression Problems},
   year = {2015},
   month = {1},
   day = {6},
   tags = {Regression, 8.42, Unsicherheit},
   url = {fileadmin/internet/fachabteilungen/abteilung_8/8.4_mathematische_modellierung/Publikationen_8.4/BPGWP1.pdf},
   web_url = {http://www.ptb.de/emrp/new04.html},
   institution = {EMRP NEW04},
   author = {Elster, C and Klauenberg, K and Walzel, M and Harris, P M and Cox, M G and Matthews, C and Wright, L and Allard, A and Fischer, N and Ellison, S and Wilson, P and Pennecchi, F and Kok, G J P and Van der Veen, A and Pendrill, L}
}

@Article { Klauenberg2015,
   title = {Informative prior distributions for ELISA analyses},
   journal = {Biostatistics},
   year = {2015},
   month = {1},
   day = {1},
   volume = {16},
   number = {3},
   pages = {454--64},
   abstract = {Immunoassays are capable of measuring very small concentrations of substances in solutions and have an immense range of application. Enzyme-linked immunosorbent assay (ELISA) tests in particular can detect the presence of an infection, of drugs, or hormones (as in the home pregnancy test). Inference of an unknown concentration via ELISA usually involves a non-linear heteroscedastic regression and subsequent prediction, which can be carried out in a Bayesian framework. For such a Bayesian inference, we are developing informative prior distributions based on extensive historical ELISA tests as well as theoretical considerations. One consideration regards the quality of the immunoassay leading to two practical requirements for the applicability of the priors. Simulations show that the additional prior information can lead to inferences which are robust to reasonable perturbations of the model and changes in the design of the data. On real data, the applicability is demonstrated across different laboratories, for different analytes and laboratory equipment as well as for previous and current ELISAs with sigmoid regression function. Consistency checks on real data (similar to cross-validation) underpin the adequacy of the suggested priors. Altogether, the new priors may improve concentration estimation for ELISAs that fulfill certain design conditions, by extending the range of the analyses, decreasing the uncertainty, or giving more robust estimates. Future use of these priors is straightforward because explicit, closed-form expressions are provided. This work encourages development and application of informative, yet general, prior distributions for other types of immunoassays.},
   tags = {Regression, 8.42, ELISA},
   web_url = {http://biostatistics.oxfordjournals.org/content/16/3/454},
   ISSN = {1468-4357},
   DOI = {10.1093/biostatistics/kxu057},
   author = {Klauenberg, K and Walzel, M and Ebert, B and Elster, C}
}

@Article { Kok2015,
   title = {Bayesian analysis of a flow meter calibration problem},
   journal = {Metrologia},
   year = {2015},
   month = {1},
   day = {2},
   volume = {52},
   number = {2},
   pages = {392-399},
   tags = {Regression, 8.42, Unsicherheit},
   web_url = {http://iopscience.iop.org/article/10.1088/0026-1394/52/2/392},
   publisher = {IOP Publishing},
   ISSN = {0026-1394},
   DOI = {10.1088/0026-1394/52/2/392},
   author = {Kok, G J P and van der Veen, A M H and Harris, P M and Smith, I M and Elster, C}
}

@Article { Klauenberg2015_3,
   title = {A tutorial on Bayesian Normal linear regression},
   journal = {Metrologia},
   year = {2015},
   month = {1},
   day = {7},
   volume = {52},
   number = {6},
   pages = {878--892},
   abstract = {Regression is a common task in metrology and often applied to calibrate instruments, evaluate inter-laboratory comparisons or determine fundamental constants, for example. Yet, a regression model cannot be uniquely formulated as a measurement function, and consequently the Guide to the Expression of Uncertainty in Measurement (GUM) and its supplements are not applicable directly. Bayesian inference, however, is well suited to regression tasks, and has the advantage of accounting for additional a priori information, which typically robustifies analyses. Furthermore, it is anticipated that future revisions of the GUM shall also embrace the Bayesian view.Guidance on Bayesian inference for regression tasks is largely lacking in metrology. For linear regression models with Gaussian measurement errors this tutorial gives explicit guidance. Divided into three steps, the tutorial first illustrates how a priori knowledge, which is available from previous experiments, can be translated into prior distributions from a specific class. These prior distributions have the advantage of yielding analytical, closed form results, thus avoiding the need to apply numerical methods such as Markov Chain Monte Carlo. Secondly, formulas for the posterior results are given, explained and illustrated, and software implementations are provided. In the third step, Bayesian tools are used to assess the assumptions behind the suggested approach.These three steps (prior elicitation, posterior calculation, and robustness to prior uncertainty and model adequacy) are critical to Bayesian inference. The general guidance given here for Normal linear regression tasks is accompanied by a simple, but real-world, metrological example. The calibration of a flow device serves as a running example and illustrates the three steps. It is shown that prior knowledge from previous calibrations of the same sonic nozzle enables robust predictions even for extrapolations.},
   tags = {8.42, Regression, Unsicherheit},
   DOI = {10.1088/0026-1394/52/6/878},
   author = {Klauenberg, K and W{\"u}bbeler, G and Mickan, B and Harris, P and Elster, C}
}

@Article { Bodnar2014,
   title = {On the adjustment of inconsistent data using the Birge ratio},
   journal = {Metrologia},
   year = {2014},
   volume = {51},
   number = {5},
   pages = {516--521},
   tags = {8.42,KC,Regression, Unsicherheit},
   web_url = {http://iopscience.iop.org/article/10.1088/0026-1394/51/5/516},
   publisher = {IOP Publishing},
   language = {en},
   ISBN = {doi:10.1088/0026-1394/51/5/516},
   ISSN = {0026-1394},
   DOI = {10.1088/0026-1394/51/5/516},
   author = {Bodnar, O and Elster, C}
}

@Article { Eichstadt2014a,
   title = {Reliable uncertainty evaluation for ODE parameter estimation - a comparison},
   journal = {Journal of Physics: Conference Series},
   year = {2014},
   volume = {490},
   number = {1},
   pages = {012230},
   keywords = {Regression, ODE, parameter identification, dynamic calibration, modelling},
   tags = {8.42,Dynamik, Regression},
   web_url = {http://iopscience.iop.org/article/10.1088/1742-6596/490/1/012230},
   publisher = {IOP Publishing},
   language = {en},
   ISSN = {1742-6596},
   DOI = {10.1088/1742-6596/490/1/012230},
   author = {Eichst{\"a}dt, S and Elster, C}
}

@Article { Heidenreich2014a,
   title = {A surrogate model enables a Bayesian approach to the inverse problem of scatterometry},
   journal = {J. Phys. Conf. Ser.},
   year = {2014},
   volume = {490},
   number = {1},
   pages = {012007},
   tags = {8.43,Bayes,Scatter-Inv,Regression,8.42, UQ},
   web_url = {http://iopscience.iop.org/article/10.1088/1742-6596/490/1/012007},
   publisher = {IOP Publishing},
   language = {en},
   ISSN = {1742-6596},
   DOI = {10.1088/1742-6596/490/1/012007},
   author = {Heidenreich, S and Gross, H and Henn, M-A and Elster, C and B{\"a}r, M}
}

@Article { Matthews2014e,
   title = {Mathematical modelling to support traceable dynamic calibration of pressure sensors},
   journal = {Metrologia},
   year = {2014},
   volume = {51},
   number = {3},
   pages = {326-338},
   keywords = {dynamic measurement, pressure, parametric model},
   tags = {8.42, Dynamik, Regression},
   url = {fileadmin/internet/fachabteilungen/abteilung_8/8.4_mathematische_modellierung/Publikationen_8.4/Mathematical_Modelling_Dynamic_Pressure_preprint.pdf},
   web_url = {http://iopscience.iop.org/article/10.1088/0026-1394/51/3/326},
   publisher = {IOP Publishing},
   language = {en},
   ISBN = {doi:10.1088/0026-1394/51/3/326},
   ISSN = {0026-1394},
   DOI = {10.1088/0026-1394/51/3/326},
   author = {Matthews, C and Pennecchi, F and Eichst{\"a}dt, S and Malengo, A and Esward, T and Smith, I M and Elster, C and Knott, A and Arrh{\'e}n, F and Lakka, A}
}

@Article { Wubbeler2013,
   title = {Simplified evaluation of magnetic field fluctuation thermometry},
   journal = {Measurement Science and Technology},
   year = {2013},
   volume = {24},
   number = {11},
   pages = {115004},
   tags = {8.42,Bayes,MFFT,Regression, Unsicherheit},
   web_url = {http://iopscience.iop.org/article/10.1088/0957-0233/24/11/115004},
   publisher = {IOP Publishing},
   language = {en},
   ISSN = {0957-0233},
   DOI = {10.1088/0957-0233/24/11/115004},
   author = {W{\"u}bbeler, G and Elster, C}
}

@Article { Wubbeler2012,
   title = {Analysis of magnetic field fluctuation thermometry using Bayesian inference},
   journal = {Measurement Science and Technology},
   year = {2012},
   volume = {23},
   number = {12},
   pages = {125004},
   tags = {8.42,Bayes,MFFT,Regression, Unsicherheit},
   web_url = {http://iopscience.iop.org/article/10.1088/0957-0233/23/12/125004},
   publisher = {IOP Publishing},
   language = {en},
   ISSN = {0957-0233},
   DOI = {10.1088/0957-0233/23/12/125004},
   author = {W{\"u}bbeler, G and Schm{\"a}hling, F and Beyer, J and Engert, J and Elster, C}
}

@Article { Elster2011a,
   title = {Bayesian uncertainty analysis for a regression model versus application of GUM Supplement 1 to the least-squares estimate},
   journal = {Metrologia},
   year = {2011},
   volume = {48},
   number = {5},
   pages = {233--240},
   tags = {8.42, Regression, Unsicherheit},
   web_url = {http://iopscience.iop.org/article/10.1088/0026-1394/48/5/001},
   publisher = {IOP Publishing},
   language = {en},
   ISSN = {0026-1394},
   DOI = {10.1088/0026-1394/48/5/001},
   author = {Elster, C and Toman, B}
}

@Article { Lira2007,
   title = {Probabilistic and least-squares inference of the parameters of a straight-line model},
   journal = {Metrologia},
   year = {2007},
   volume = {44},
   number = {5},
   pages = {379--384},
   tags = {8.42,Bayes,Regression,Unsicherheit},
   web_url = {http://iopscience.iop.org/article/10.1088/0026-1394/44/5/014},
   publisher = {IOP Publishing},
   language = {en},
   ISSN = {0026-1394},
   DOI = {10.1088/0026-1394/44/5/014},
   author = {Lira, I and Elster, C and W{\"o}ger, W}
}