On the foundations of the physical probability concept

Most physiological scientists have restricted understanding of probability as relative frequency in a large collection (for example, of atoms). Most appropriate for the relatively circumscribed problems of the physical sciences, this understanding of probability as a physical property has conveyed the widespread impression that the "proper" statistical "method" can eliminate uncertainty by determining the "correct" frequency or frequency distribution. However, many relatively recent developments in the theory of probability and decision making deny such exalted statistical ability. Proponents of Bayes's subjectivist theory, for example, assert that probability is "degree of belief," a more tentative idea than relative frequency or physical probability, even though degree of belief assessment may utilize frequency information. In the subjectivist view, probability and statistics are means of expressing a consistent opinion (a probability) to handle uncertainty but never means to eliminate it. In the physiological sciences the contrast between the two views is critical, because problems dealt with are generally more complex than those of physics, requiring judgments and decisions. We illustrate this in testing the efficacy of penicillin by showing how the physical probability method of "hypothesis testing" may contribute to the erroneous idea that science consists of "verified truths" or "conclusive evidence" and how this impression is avoided in subjectivist probability analysis.

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Computing under-ice discharge: A proof-of-concept using hydroacoustics and the Probability Concept

Journal of Hydrology ◽

10.1016/j.jhydrol.2018.04.073 ◽

2018 ◽

Vol 562 ◽

pp. 733-748 ◽

Cited By ~ 2

Author(s):

John W. Fulton ◽

Mark F. Henneberg ◽

Taylor J. Mills ◽

Michael S. Kohn ◽

Brian Epstein ◽

...

Keyword(s):

Proof Of Concept ◽

Probability Concept

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Subjective Probability and Geometry: Three Metric Theorems Concerning Random Quantities

Journal of Mathematics Research ◽

10.5539/jmr.v10n3p7 ◽

2018 ◽

Vol 10 (3) ◽

pp. 7

Author(s):

Pierpaolo Angelini ◽

Angela De Sanctis

Keyword(s):

Random Quantity ◽

Real Space ◽

Geometric Interpretation ◽

Extensive Study ◽

Dimensional Structure ◽

Interpretation Of Probability ◽

Straight Line ◽

Probability Concept ◽

Deep Meaning ◽

Unit Vectors

Affine properties are more general than metric ones because they are independent of the choice of a coordinate system. Nevertheless, a metric, that is to say, a scalar product which takes each pair of vectors and returns a real number, is meaningful when $n$ vectors, which are all unit vectors and orthogonal to each other, constitute a basis for the $n$-dimensional vector space $\mathcal{A}$. In such a space $n$ events $E_i$, $i = 1, \ldots, n$, whose Cartesian coordinates turn out to be $x^i$, are represented in a linear form. A metric is also meaningful when we transfer on a straight line the $n$-dimensional structure of $\mathcal{A}$ into which the constituents of the partition determined by $E_1, \ldots, E_n$ are visualized. The dot product of two vectors of the $n$-dimensional real space $\mathbb{R}^n$ is invariant: of these two vectors the former represents the possible values for a given random quantity, while the latter represents the corresponding probabilities which are assigned to them in a subjective fashion.We deduce these original results, which are the foundation of our next and extensive study concerning the formulation of a geometric, well-organized and original theory of random quantities, from pioneering works which deal with a specific geometric interpretation of probability concept, unlike the most part of the current ones which are pleased to keep the real and deep meaning of probability notion a secret because they consider a success to give a uniquely determined answer to a problem even when it is indeterminate.Therefore, we believe that it is inevitable that our references limit themselves to these pioneering works.

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