Browsing by Author "Grientschnig, Dieter"
Now showing 1 - 5 of 5
Results Per Page
Sort Options
- ItemCoverage intervals according to MARLAP, Bayesian statistics and the new ISO 11929 for ionising radiation measurements(PERGAMON-ELSEVIER SCIENCE LTD, 2012) Grientschnig, Dieter; Lira, IgnacioThe coverage intervals stipulated by ISO 11929 (2010) for estimating the uncertainty from ionising radiation measurements of replicate samples are compared with those of MARLAP (= Multi-Agency Radiological Laboratory Analytical Protocols Manual) and of Bayesian statistics. The latter two intervals agree well despite their different concepts. Whereas for either of them the ratio of the length of the coverage interval and MARLAP's standard uncertainty grows when the number of samples decreases, no such growth arises for the interval mandated by ISO 11929 (2010). It may therefore be too short (e.g. for three samples by a factor of approximately 2). (C) 2011 Elsevier Ltd. All rights reserved.
- ItemNon-informative priors in GUM Supplement 1(ELSEVIER SCI LTD, 2011) Lira, Ignacio; Grientschnig, DieterSupplement 1 to the 'Guide to the Expression of Uncertainty in Measurement' (GUM S1) proposes a Monte Carlo method for the propagation of the probability density functions (PDFs) assigned to the input quantities that are related to an output quantity through a measurement model. Guidance is provided in GUM Si for assigning PDFs to the input quantities for which data but no prior knowledge are available. The procedure relies on Bayes' theorem and on the use of appropriate non-informative priors. An inconsistency in the choice of such priors is pointed out. (C) 2011 Elsevier Ltd. All rights reserved.
- ItemReassessment of a calibration model by Bayesian reference analysis(2011) Grientschnig, Dieter; Lira, IgnacioThe Bayesian analysis of a simple calibration model is reconsidered. Observed values are at hand that conform to a Gaussian probability distribution of unknown standard deviation S. The mean of this distribution is given by a polynomial function of the measurand Y. For the coefficients P of this polynomial a state-of-knowledge distribution is available, whereas no prior information about Y and S exists. A conditional reference prior for (Y, S) given P is derived. It shows no functional dependence on the measurand in the case that the calibration function is linear, but depends non-trivially on the measurand otherwise. This prior is compared with other priors that have been used in the literature to analyse the same calibration model. It leads to a different posterior distribution than the application of Supplement 1 to the 'Guide to the Expression of Uncertainty in Measurement'. An example illustrates differences of results founded on the various non-informative priors.
- ItemRevision of 'Reassessment of a calibration model by Bayesian reference analysis'(2012) Grientschnig, Dieter; Lira, IgnacioIn a previous paper (2011 Metrologia 48 L7-11) we have calculated a reference prior for a calibration model where a state-of-knowledge distribution of the coefficients of the calibration function is provided. Observed values of the response for a fixed value of the stimulus are also available. They are assumed to conform to a Gaussian probability distribution of unknown standard deviation. The calculation of the reference prior is revised here using a different sequence of subsets of the parameter space. This choice is preferable to the earlier one with respect to the properties of the ensuing posterior. In contrast to the former result the revised reference prior leads to the same posterior distribution as the application of Supplement 1 to the 'Guide to the Expression of Uncertainty in Measurement'.
- ItemThe Cosine Error: A Bayesian Procedure for Treating a Non-repetitive Systematic Effect(2016) Lira Canguilhem, Ignacio; Grientschnig, Dieter