Notes on Measurement Fundamentals: A Pragmatic View

This paper [@mari:2012:measurement], was referenced in the “Quality of Measurment” results paper [@maul:2017:quality]. This paper presents the ‘structural’ view of measurement that is specialized in the ‘Quality’ paper. This paper attempts to move beyond representation views of measurement and towards a pragmatic theory, similar to the concepts in Hand’s book [@hand:2004:measurement]. It’s scope of ambition is similar

Like the “Quality” paper, this paper makes a distinction between evaluation and measurement. Evaluation is modeled on function evaluation.

it is well known that in quantum physics the relations between causality and measurement uncertainty are much more complex, but we will not consider this subject here

As a basic fact, the relation between objects under measurement and measurement results is generally many-to-many, i.e., the same object can be evaluated to different results, and different objects can be evaluated to the same result.

The notion of a many-to-many relationship seems to contrast with the causal relationship posited between object and result.

Again, the paper repeats the notion that measurement uncertainty is the proper summary of the inter-subjective aspects of an empirical demonstration.

The paper breaks the measurement development process into the ‘modeling’ stage and the ‘operative’ stage. The modeling stage corresponds to method development, while the operative stage corresponds to method deployment. The method validation step is not mentioned. In chemical measurement, validation corresponds to providing evidence on inter-subjective validity.

In the simplest case, the measuring instrument input is the measurand, so that the two operative steps are sometimes considered as inverse with one another: the experimental step instances the transduction function, which is then inverted in the representational step which, for this reason, is sometimes called measurand reconstruction. According to this perspective, the whole operative stage of measurement is said to implement an identity function. This position is in fact wrong because of a wrong ontological superposition: the measuring instrument input is the measurand, i.e, a property, not its value.

This implicitly raises a critique of the Bayesian theory of measurement, where a posterior distribution of the measurement result is a transformation of the prior, with the likelihood playing the role of map from ‘property’ to ‘indicator’, and the Bayesian inversion the role of ‘measurand reconstruction’. So how is the ‘property,’ an empirical quantity, lifted to a ‘prior distribution’, a mathematical quantity? Furthermore, there is an algebraic structure on ‘amount of substance.’ In indirect measurement, the likelihood function maps between two related ‘properties’ - the ‘nominal’ map of ‘particles’ to ‘chemical types’, and the relationship between ‘chemical type’ and ‘indicator’. There is an implicit role for an ‘index’ - a specific region of space-time that is the object of measurement. The purely subjective Bayesian theory does not have a necessary link to the map between the actual measurand and the prior distribution on the measurand. Does the ‘reference prior’ approach solve this issue? How does ‘maximum entropy’ compare to the ‘reference prior’ approach? My sense is that Bernardo intended reference analysis to be a generalization of the maximum entropy approach.

The process of measurement as symbolization; the meaning of the symbol derived from the pragmatic maxim.

Whenever such a theory is not available, not an uncommon case in soft measurement, measurement validation becomes a critical issue: an objective support has to be given to the claim that measurement results actually refer to the stated measurand.

This claim puts validation as establishing the relationship between the measurand and the indicator as ‘objective support’. As practiced, chemical measurement validation is more focused on the inter-subjective aspects, but it’s probably a mistake to think of these as independent.