By Franco (EDT)/ Forbes, Alistair B. (EDT) Pavese
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Additional info for Advances in Data Modeling for Measurements in the Metrology and Testing Fields
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. In model (7), Λ = (Λ(1) , . . , Λ(N ) ) contains the parameters of the N participants’ pdfs and the π i are positive proportions summing to unity. It may often be appropriate to take these 35 Actually in most cases only of the (yh – yr ), where yr is the value attributed to a reference standard, generally a transfer standard.
N ) ) contains the parameters of the N participants’ pdfs and the π i are positive proportions summing to unity. It may often be appropriate to take these 35 Actually in most cases only of the (yh – yr ), where yr is the value attributed to a reference standard, generally a transfer standard. 24 F. Pavese proportions to be equal; that is, πi = 1/N , i = 1, . , N . Speciﬁc metrological reasoning may indicate unequal proportions. In key comparisons, the KCRV is given as the expectation value of the density function.
21) If we assume a uniform distribution for x 7 , we obtain p(x|y) ∝ p(y|x). (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.