Advanced Mathematical and Computational Tools in Metrology by P. Ciarlini, M. G. Cox, F. Pavese, G. B. Rossi

By P. Ciarlini, M. G. Cox, F. Pavese, G. B. Rossi

This quantity collects refereed contributions in accordance with the shows made on the 6th Workshop on complex Mathematical and Computational instruments in Metrology, held on the Istituto di Metrologia "G. Colonnetti" (IMGC), Torino, Italy, in September 2003. It presents a discussion board for metrologists, mathematicians and software program engineers that might inspire a more beneficial synthesis of abilities, features and assets, and promotes collaboration within the context of european programmes, EUROMET and EA tasks, and MRA necessities. It includes articles via a big, world wide staff of metrologists and mathematicians all in favour of dimension technology and, including the 5 earlier volumes during this sequence, constitutes an authoritative resource for the mathematical, statistical and software program instruments essential to glossy metrology.

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P > 1, it is necessary to define a measure M(X) as in (4). Rather than define ad hoc measures, we consider ones having a probabilistic justification. We make the further assumption about the model (1) that E N(O,V(X)). Then, given data y E Y ,the probability p(yla,A) that the data arose from parameters (a,A) is given by N and the log likelihood L(a,Xly) by The maximum likelihood (ML) estimates of a and X are determined by maximizing the probability p(yla,A) which is equivalent to minimizing -L(a, Xly) with respect to a and A.

This work was undertaken as part of the Software Support for Metrology and Quantum Metrology programmes, funded by the United Kingdom Department of Trade and Industry. 1. Introduction Least squares analysis methods are widely used in metrology and are justified for a large number of applications on the basis of both statistical theory and practical experience. Given a model specified by parameters a, measurement data values and their associated uncertainty matrix, it is possible to define a least squares analysis (LSA) method that gives the measurement data values the appropriate ‘degreeof belief’ as specified by the uncertainty *Work partially funded under EU SofIbolsMetroNet Contract N.

In such exercises, the conformity of the model and input data is of great concern since, due to the complex functional inter-relationships, an invalid input could have a significant effect on a number of parameter estimates. 3. Adjustment procedures In this section, we consider ways of adjusting the input information y and V in order to achieve conformity of the least squares solution. We regard the least squares estimate a = a(y,V ) as a function of the measurements y and the input uncertainty matrix V.

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