By Franco (EDT)/ Forbes, Alistair B. (EDT) Pavese
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Extra resources for Advances in Data Modeling for Measurements in the Metrology and Testing Fields
These peculiar observations are not viewed as outliers, but as the eﬀect of an admissible variability. Consider a ﬁnite mixture of densities as a linear superposition of N component densities (named a mixture density in the following). In an intercomparison, suppose that, for i = 1, . . , N , a density function fi (x; Λ(i) ) is provided for participant i, where Λ(i) is the (row) vector of Λi , say, parameters of fi . Then the mixture density N πi fi (x; Λ(i) ), g(x; Λ) = (7) i=1 where (Λ,π) are the mixture parameters, g is assumed to characterise the total data variability related to the output pdf.
22) So maximizing p(x|y) with respect to x, in view of (22), is computationally equivalent to maximizing p(y|x), that is, to searching x ˆ such that p(y|ˆ x) = max p(y|x). x (23) But, for Gauss, if formula (23) may be used for computing x ˆ, the meaning of x ˆ is still established by formula (20). Fisher changes this perspective completely, although obtaining, in this case, the same ﬁnal result. He argues that the Bayes–Laplace rule (21) can not be applied, unless it is possible to determine an ‘objective’ prior distribution, p(x), for x.
A full exploitation of the concept of using bounding intervals, particularly useful in the treatment of systematic errors, is developed in Chapter 4 of this book. Interval statistics, in turn, can be seen as a particular case of fuzzy statistics ([ABF04] and this book Chapter 7). , [UW03]. 2 Speciﬁc problems and outcomes of the intercomparisons, namely the MRA key comparisons In Figure 1 the process, from planning to outcomes, of a comparison is summarised. As can be found in more detail in [Pav06, Pav07], the basic steps of this process are the following.
Advances in Data Modeling for Measurements in the Metrology and Testing Fields by Franco (EDT)/ Forbes, Alistair B. (EDT) Pavese