Browsing by Author "Woeger, Wolfgang"

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    Comparison between the conventional and Bayesian approaches to evaluate measurement data
    (2006) Lira, Ignacio; Woeger, Wolfgang
    Measurement data subject only to random effects can be evaluated within the frameworks of conventional as well as Bayesian statistical theory. In this paper, both viewpoints are presented and examples including Gaussian, uniform and Poisson statistics are discussed. The cases of data produced by different observers, and of quantities expressed by measurement models involving systematic effects, are also briefly touched upon. It is shown that, although in most practical cases the uncertainty intervals obtained from repeated measurements using either theory may be similar, their interpretation is completely different. Since the Bayesian approach treats random and systematic effects in the same way, the authors claim that it is more flexible and better adapted to practice than conventional theory.
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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.