This file was created by the TYPO3 extension bib --- Timezone: CEST Creation date: 2024-04-19 Creation time: 03-26-53 --- Number of references 32 article KastnerMHMPCWHRE2023 Measurement Science and Technology 2023 9 21 8.4,8.42,LargeScaleDataAna,Regression accepted 10.1088/1361-6501/acfc27 BKästner MMarschall AHornemann SMetzner PPatoka SCortes GWübbeler AHoehl ERühl CElster article WubbelerMRKE2021 Measurement Science and Technology 2021 12 24 33 035402 8.4,8.42,LargeScaleDataAna,Regression accepted 10.1088/1361-6501/ac407a GWübbeler MMarschall ERühl BKästner CElster phdthesis Metzner2021 2021 12 7 publiziert 8.4,8.42,Messunsicherheit,Regression,Fingerprinting,LargeScaleDataAna TU Berlin PhD Thesis 10.14279/depositonce-12455 SMetzner article KlauenbergMBCvE2021 Measurement 2021 11 6 187 110340 8.4,8.42,Regression 0263-2241 10.1016/j.measurement.2021.110340 KKlauenberg SMartens ABošnjaković M.GCox A. M.Hvan der Veen CElster article MetznerWFGKE2021 Physics in Medicine & Biology 2021 3 1 66 7 075006 8.4,8.42,Messunsicherheit,Regression,Fingerprinting,LargeScaleDataAna 10.1088/1361-6560/abeae7 SMetzner GWübbeler SFlassbeck CGatefait CKolbitsch CElster article WubbelerE2020_2 Metrologia 2021 1 7 58 1 014002 online 8.4,8.42,Regression,LargeScaleDataAna accepted 10.1088/1681-7575/abc97b GWübbeler CElster article MarschallHWHRKE2020 Opt. Express 2020 12 10 26 28 38762--38772 8.4,8.42,Regression,LargeScaleDataAna 10.1364/OE.404959 MMarschall AHornemann GWübbeler AHoehl ERühl BKästner CElster techreport MartensKE2020 2020 11 15 8.4,8.42,Regression http://empir.npl.co.uk/emue/wp-content/uploads/sites/49/2020/12/Compendium_M27.pdf Adriaan M.H. van der Veen, Maurice G. Cox

Teddington, United Kingdom

M27 E14 Good Practice in Evaluating Measurement uncertainty - Compendium of examples SMartens KKlauenberg CElster techreport MartensKNCEE2020 2020 11 15 8.4,8.42,Regression http://empir.npl.co.uk/emue/wp-content/uploads/sites/49/2020/12/Compendium_M27.pdf Adriaan M.H. van der Veen, Maurice G. Cox

Teddington, United Kingdom

M27 E13 Good Practice in Evaluating Measurement uncertainty - Compendium of examples SMartens KKlauenberg JNeukammer SCowen S L REllison CElster techreport MartensKMYFE2020 2020 11 15 8.4,8.42,Regression http://empir.npl.co.uk/emue/wp-content/uploads/sites/49/2020/12/Compendium_M27.pdf Adriaan M.H. van der Veen, Maurice G. Cox

Teddington, United Kingdom

M27 E11 Good Practice in Evaluating Measurement uncertainty - Compendium of examples SMartens KKlauenberg BMickan CYardin NFischer CElster article BartlEMSVW2020 Measurement Science and Technology 2020 4 3 31 6 8.4,8.42,Unsicherheit,Regression 10.1088/1361-6501/ab7359 GBartl CElster JMartin RSchödel MVoigt AWalkov article LehnertKWCSE2019 SIAM J. Imaging Sci. 2019 12 12 12 4 2035--2062 8.4,8.42,Regression,LargeScaleDataAna 10.1137/19M1246274 JudithLehnert ChristophKolbitsch GerdWübbeler AmedeoChiribiri TobiasSchäffter ClemensElster article MetznerWE2018 AStA Adv Stat Anal 2019 8 29 103 3 333--355 8.4,8.42,Messunsicherheit,Regression,Fingerprinting,LargeScaleDataAna 10.1007/s10182-018-00334-0 SMetzner GWübbeler CElster article MartinBE2019 Measurement Science and Technology 2019 2 21 30 045012 8.4,8.42,Unsicherheit,Regression 10.1088/1361-6501/ab094b JMartin GBartl CElster article LehnertWKCCESSE2018 Physics in Medicine & Biology 2018 10 10 63 215017 8.4, 8.42,Regression,LargeScaleDataAna 10.1088/1361-6560/aae758 JLehnert GWübbeler CKolbitsch AChiribiri LCoquelin GEbrard NSmith TSchäffter CElster article WubbelerBE2018 Metrologia 2018 1 2 55 1 20 8.4,8.42,Unsicherheit,Regression 10.1088/1681-7575/aa98aa GWübbeler OBodnar CElster article ElsterW2017 Comput. Stat. 2017 1 3 32 1 51--69 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. random coefficient regression, Bayesian inference, noninformative prior 8.42, Regression 10.1007/s00180-015-0641-3 CElster GWübbeler article DierlEFKEE2016 Journal of the Optical Society of America A 2016 6 23 33 7 1370--1376 dynamic measurement, dynamic uncertainty, deconvolution 8.42, Dynamik, Regression 10.1364/JOSAA.33.001370 MDierl TEckhard BFrei MKlammer SEichstädt CElster article Elster2016a Metrologia 2016 1 2 53 1 S10 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. 8.4, 8.42, Unsicherheit, Regression http://stacks.iop.org/0026-1394/53/i=1/a=S10 10.1088/0026-1394/53/1/S10 CElster GWübbeler article Klauenberg2016 Metrologia 2016 1 3 53 1 S32 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. Bayesian, MCMC, Markov chain Monte Carlo 8.42, Unsicherheit, Regression http://stacks.iop.org/0026-1394/53/i=1/a=S32 10.1088/0026-1394/53/1/S32 KKlauenberg CElster techreport NEW04_Bayes 2015 1 6 Regression, 8.42, Unsicherheit fileadmin/internet/fachabteilungen/abteilung_8/8.4_mathematische_modellierung/Publikationen_8.4/BPGWP1.pdf http://www.ptb.de/emrp/new04.html EMRP NEW04 CElster KKlauenberg MWalzel P MHarris M GCox CMatthews LWright AAllard NFischer SEllison PWilson FPennecchi G J PKok AVan der Veen LPendrill article Klauenberg2015 Biostatistics 2015 1 1 16 3 454--64 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. Regression, 8.42, ELISA http://biostatistics.oxfordjournals.org/content/16/3/454 1468-4357 10.1093/biostatistics/kxu057 KKlauenberg MWalzel BEbert CElster article Kok2015 Metrologia 2015 1 2 52 2 392-399 Regression, 8.42, Unsicherheit http://iopscience.iop.org/article/10.1088/0026-1394/52/2/392 IOP Publishing 0026-1394 10.1088/0026-1394/52/2/392 G J PKok A M Hvan der Veen P MHarris I MSmith CElster article Klauenberg2015_3 Metrologia 2015 1 7 52 6 878--892 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. 8.42, Regression, Unsicherheit 10.1088/0026-1394/52/6/878 KKlauenberg GWübbeler BMickan PHarris CElster article Bodnar2014 Metrologia 2014 51 5 516--521 8.42,KC,Regression, Unsicherheit http://iopscience.iop.org/article/10.1088/0026-1394/51/5/516 IOP Publishing en doi:10.1088/0026-1394/51/5/516 0026-1394 10.1088/0026-1394/51/5/516 OBodnar CElster article Eichstadt2014a Journal of Physics: Conference Series 2014 490 1 012230 Regression, ODE, parameter identification, dynamic calibration, modelling 8.42,Dynamik, Regression http://iopscience.iop.org/article/10.1088/1742-6596/490/1/012230 IOP Publishing en 1742-6596 10.1088/1742-6596/490/1/012230 SEichstädt CElster article Heidenreich2014a J. Phys. Conf. Ser. 2014 490 1 012007 8.43,Bayes,Scatter-Inv,Regression,8.42, UQ http://iopscience.iop.org/article/10.1088/1742-6596/490/1/012007 IOP Publishing en 1742-6596 10.1088/1742-6596/490/1/012007 SHeidenreich HGross M-AHenn CElster MBär article Matthews2014e Metrologia 2014 51 3 326-338 dynamic measurement, pressure, parametric model 8.42, Dynamik, Regression fileadmin/internet/fachabteilungen/abteilung_8/8.4_mathematische_modellierung/Publikationen_8.4/Mathematical_Modelling_Dynamic_Pressure_preprint.pdf http://iopscience.iop.org/article/10.1088/0026-1394/51/3/326 IOP Publishing en doi:10.1088/0026-1394/51/3/326 0026-1394 10.1088/0026-1394/51/3/326 CMatthews FPennecchi SEichstädt AMalengo TEsward I MSmith CElster AKnott FArrhén ALakka article Wubbeler2013 Measurement Science and Technology 2013 24 11 115004 8.42,Bayes,MFFT,Regression, Unsicherheit http://iopscience.iop.org/article/10.1088/0957-0233/24/11/115004 IOP Publishing en 0957-0233 10.1088/0957-0233/24/11/115004 GWübbeler CElster article Wubbeler2012 Measurement Science and Technology 2012 23 12 125004 8.42,Bayes,MFFT,Regression, Unsicherheit http://iopscience.iop.org/article/10.1088/0957-0233/23/12/125004 IOP Publishing en 0957-0233 10.1088/0957-0233/23/12/125004 GWübbeler FSchmähling JBeyer JEngert CElster article Elster2011a Metrologia 2011 48 5 233--240 8.42, Regression, Unsicherheit http://iopscience.iop.org/article/10.1088/0026-1394/48/5/001 IOP Publishing en 0026-1394 10.1088/0026-1394/48/5/001 CElster BToman article Lira2007 Metrologia 2007 44 5 379--384 8.42,Bayes,Regression,Unsicherheit http://iopscience.iop.org/article/10.1088/0026-1394/44/5/014 IOP Publishing en 0026-1394 10.1088/0026-1394/44/5/014 ILira CElster WWöger