Browsing by Author "Elster, Clemens"

Now showing 1 - 3 of 3
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    Analysis of Key Comparisons Incorporating Knowledge About Bias
    (2012) Lira Canguilhem, Ignacio; Chunovkina, Anna; Elster, Clemens; Woger, Wolfgang
    A method is proposed for analyzing key comparison data. It is based on the assumption that each laboratory participating in the comparison exercise obtains independent and consistent estimates of the measurand and that, in addition, each laboratory provides an estimate of the quantity that collects all systematic effects that the laboratory took into account. The unknown value of the latter quantity, subtracted from its estimate, is defined as the laboratory's bias. The uncertainties associated with the estimates of the measurand and with the vanishing biases' estimates are also assumed to be reported. In this paper, we show that the information provided in this way may be of help for judging the performances of the laboratories in their correction of systematic effects. This is done by developing formulas for the final (consensus) estimates and uncertainties of the measurand and of the biases. Formulas for the final estimates and uncertainties of the pairwise differences between the biases are also developed. An example involving simulated key comparison data makes apparent the benefits of the proposed approach.
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    On the choice of a noninformative prior for Bayesian inference of discretized normal observations
    (2012) Elster, Clemens; Lira, Ignacio
    We consider the task of Bayesian inference of the mean of normal observations when the available data have been discretized and when no prior knowledge about the mean and the variance exists. An application is presented which illustrates that the discretization of the data should not be ignored when their variability is of the order of the discretization step. We show that the standard (noninformative) prior for location-scale family distributions is no longer appropriate. We work out the reference prior of Berger and Bernardo, which leads to different and more reasonable results. However, for this prior the posterior also shows some non-desirable properties. We argue that this is due to the inherent difficulty of the considered problem, which also affects other methods of inference. We therefore complement our analysis by an empirical Bayes approach. While such proceeding overcomes the disadvantages of the standard and reference priors and appears to provide a reasonable inference, it may raise conceptual concerns. We conclude that it is difficult to provide a widely accepted prior for the considered problem.
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    Probabilistic and least-squares inference of the parameters of a straight-line model
    (2007) Lira, Ignacio; Elster, Clemens; Woeger, Wolfgang
    Two methods are presented by which a straight line is to be fitted to a cloud of points in Cartesian coordinates. It is assumed that data are available in the form of a series of measurements in each coordinate, together with an assessment of their covariance matrices. In the first (probabilistic) method, the joint probability density function (PDF) for the two parameters of the straight line is considered. An explicit expression for this PDF is derived; it allows one to compute numerically the expectations, the variances and the covariance between the two parameters of the straight line. The second method is that of least-squares; it renders a non-linear system of equations for the point estimates of the parameters, as well as an approximation to their covariance matrix. In contrast to least-squares, the probabilistic method allows for the exact calculation of the probability that the true values of the parameters lie within specified intervals.