Algebraic Frameworks for Measurement in the Natural Sciences

Domotor, Zoltan

doi:10.2478/v10048-012-0032-7

Cited by 3 publications

(3 citation statements)

References 11 publications

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“…. , σ 2 s , σ 2 s+1 ′ are known, based on the model assumptions and from (11) and (12), we trivially get the pivot, Wald-type statistic, useful for making statistical inference about K ′ b (e.g. testing a null hypothesis H 0 : K ′ b = K ′ b 0 for some b 0 ) and/or about the variable w = K ′ b + L ′ u with their exact (null) distribution:…”

Section: Standard Methods For Statistical Inference On Fixed and Randmentioning

confidence: 99%

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Estimation, Testing, and Prediction Regions of the Fixed and Random Effects by Solving the Henderson’s Mixed Model Equations

Witkovský¹

2012

Measurement Science Review

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We present a brief overview of the methods for making statistical inference (testing statistical hypotheses, construction of confidence and/or prediction intervals and regions) about linear functions of the fixed effects and/or about the fixed and random effects simultaneously, in conventional simple linear mixed model. The presented approach is based on solutions from the Henderson's mixed model equations.

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Section: Standard Methods For Statistical Inference On Fixed and Randmentioning

confidence: 99%

“…[44], [15], [36]), are widespread. Such applications with analytical methods based on linear mixed models include different fields of the biomedical and technical research, (see [56] and/or [11]). For illustration, here we shall mention just few of them: e.g.…”

Section: Introductionmentioning

confidence: 99%

Estimation, Testing, and Prediction Regions of the Fixed and Random Effects by Solving the Henderson’s Mixed Model Equations

Witkovský¹

2012

Measurement Science Review

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“…A close look at RTM's axioms for qualitative structures associated with measurable attributes reveals that these axioms invariably transcend simple qualitative observations and posit hypothetical infinite precisions that exceed the capacities of human measurement. (For some additional details and discussion of related issues, see [4] and [5]. )…”

Section: Conceptual Issues In the Representationalist Founda-mentioning

confidence: 99%

An Algebraic Approach to Unital Quantities and their Measurement

Domotor

Batitsky

2016

Measurement Science Review

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The goals of this paper fall into two closely related areas. First, we develop a formal framework for deterministic unital quantities in which measurement unitization is understood to be a built-in feature of quantities rather than a mere annotation of their numerical values with convenient units. We introduce this idea within the setting of certain ordered semigroups of physical-geometric states of classical physical systems. States are assumed to serve as truth makers of metrological statements about quantity values. A unital quantity is presented as an isomorphism from the target system's ordered semigroup of states to that of positive reals. This framework allows us to include various derived and variable quantities, encountered in engineering and the natural sciences. For illustration and ease of presentation, we use the classical notions of length, time, electric current and mean velocity as primordial examples. The most important application of the resulting unital quantity calculus is in dimensional analysis. Second, in evaluating measurement uncertainty due to the analog-to-digital conversion of the measured quantity's value into its measuring instrument's pointer quantity value, we employ an ordered semigroup framework of pointer states. Pointer states encode the measuring instrument's indiscernibility relation, manifested by not being able to distinguish the measured system's topologically proximal states. Once again, we focus mainly on the measurement of length and electric current quantities as our motivating examples. Our approach to quantities and their measurement is strictly state-based and algebraic in flavor, rather than that of a representationalist-style structure-preserving numerical assignment.

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Dimensional analysis in relativity and in differential geometry

Mana¹

2021

Eur. J. Phys.

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This note provides a short guide to dimensional analysis in Lorentzian and general relativity and in differential geometry. It tries to revive Dorgelo and Schouten’s notion of ‘intrinsic’ or ‘absolute’ dimension of a tensorial quantity. The intrinsic dimension is independent of the dimensions of the coordinates and expresses the physical and operational meaning of a tensor. The dimensional analysis of several important tensors and tensor operations is summarized. In particular it is shown that the components of a tensor need not have all the same dimension, and that the Riemann (once contravariant and thrice covariant) and Ricci (fully covariant) curvature tensors are dimensionless. The relation between dimension and operational meaning for the metric and stress–energy–momentum tensors is discussed; and the main conventions for the dimensions of these two tensors and of Einstein's constant are reviewed. A more thorough and updated analysis is available as a preprint.

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Algebraic Frameworks for Measurement in the Natural Sciences

Cited by 3 publications

References 11 publications

Estimation, Testing, and Prediction Regions of the Fixed and Random Effects by Solving the Henderson’s Mixed Model Equations

Estimation, Testing, and Prediction Regions of the Fixed and Random Effects by Solving the Henderson’s Mixed Model Equations

An Algebraic Approach to Unital Quantities and their Measurement

Dimensional analysis in relativity and in differential geometry

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