The applications of the LSA for adjusting values are very wide. My interest is limited here to the field of quantitative measurements and for two peculiar fields of high-accuracy measurements, where it is used for computing adjusted values of the so-called “universal constants” (CODATA task) and of the atomic masses (often called atomic weights) (AME, AMDC task), for two purposes: to obtain an evaluation the consistency with each other of these (large) sets of values with a minimised associated uncertainty; to provide a set of recommended values. I report at the end some basic references about these two frames and their use of the LSA.
The LSA is used for minimising, according to a L2 norm, the standard deviation of a set, by computing new values (or deviations from the original values, called “adjustments”) of each member of the set of quantities, and the new uncertainty associated to each member of the set—generally lower, thanks to the minimisation.
However, the system cannot provide ‘absolute’ adjusted values when any of the values can be assumed to be ‘exact’. In fact, at least one of the original values must be kept constant, so, in actuality, all the adjustments are relative to this member, taken as ‘reference’ (please note, this does not generally mean ‘exact’). Should another member be chosen as the fixed one, all adjustments would be different, with a peculiar characteristics: the differences between two members of the set still remain the same, irrespective to the choice of the reference. Sometimes more than one member is kept fixed: I skip here this case for simplicity.
This ambiguity stands unless an additional assumption is made, concerning the ‘best’ reference, ‘best’ according to a chosen criterium. This limitation arises directly from the fact that, in measurement, the ‘true’ value cannot be known; consequently, no objective way exist to state which member carries the correct numerical value, implying that its value should not be adjusted. In the case of the use of fundamental constants for the definition of the measurement units, the additional assumption might consist of an independent way to estimate the minimisation of the discontinuity between the units, before and after the change in definition, which should strictly be avoided.
In my opinion, the LSA is a sound method to evaluate the consistency of the set of values with the lowest associated uncertainty level, by taking advantage of the statistical properties of a larger overall set. On the contrary, as to obtain and recommend ‘best’ values for standard tables of nuclides or of fundamental constants, the fact that the LSA evaluation is biased by the arbitrary choice of the reference member(s) should be carefully taken in consideration: in my opinion this bias makes the method inappropriate for that purpose, with respect to statistical means to obtain the ‘best value’ for each member of the set. In addition, with the LSA a relationship is construed between all members of the set, which could conflict with the fact that they originally are, at least in part, independent with each other.
Some basic and latest references:
CODATA: http://physics.nist.gov/cuu/Constants/index.html, http://www.bipm.org/extra/codata/. Last adjustment: P.J. Mohr, B.N. Taylor and D.B. Newell, CODATA Recommended Values of the Fundamental Physical Constants: 2010, Rev. Modern Phys. 84 (2012) 1–94. LSA application: Cohen E R, Crowe K M and DuMond J W M 1957 The Fundamental Constants of Physics (Tamworth, UK: G. & J. Chesters); C. Eisenhart Spec.Publ. 300 NBS paper 4.5 (1961); F. Pavese, Metrologia 51 (2014) L1–L4.
AME, AMDC: http://www-csnsm.in2p3.fr/amdc/. Adjustments using LSA: A.H. Wapstra, G. Audi and C. Thibault, Nucl. Phys. A 729 (2003) 129, M. Wang, G. Audi, A.H. Wapstra, F.G. Kondev, M. MacCormick, X. Xu and B. Pfeiffer, Chinese Phys C 36 (2012) 1603.
sorry I do not have the expertise to answer this question.
Regards
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