Teaching statistics in the physics curriculum: Unifying and clarifying role of subjective probability

@article{DAgostini1999TeachingSI,
  title={Teaching statistics in the physics curriculum: Unifying and clarifying role of subjective probability},
  author={Giulio D'Agostini},
  journal={American Journal of Physics},
  year={1999},
  volume={67},
  pages={1260-1268}
}
  • G. D'Agostini
  • Published 6 August 1999
  • Philosophy
  • American Journal of Physics
Subjective probability is based on the intuitive idea that probability quantifies the degree of belief that an event will occur. A probability theory based on this idea represents the most general framework for handling uncertainty. A brief introduction to subjective probability and Bayesian inference is given, with comments on typical misconceptions which tend to discredit it and with comparisons to other approaches. 

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References

SHOWING 1-10 OF 12 REFERENCES

The role of probability in statistical physics

Abstract In this expository paper we discuss the role of probability in statistical physics: it should be that of a general tool guiding induction and must not be restricted only to the empirical

Scientific Reasoning: The Bayesian Approach

TLDR
This new edition of Howson and Urbach's account of scientific method from the Bayesian standpoint includes chapter exercises and extended material on topics such as regression analysis, distributions densities, randomisation and conditionalisation.

Clearing up Mysteries { the Original Goal

We show how the character of a scientiic theory depends on one's attitude toward probability. Many circumstances seem mysterious or paradoxical to one who thinks that probabilities are real physical

The Theory of Probability

TLDR
This book is a searching analysis of the fundamental principles of the theory of probability and of the particular judgments involved in its application to concrete problems and is in agreement with the views expressed by Dr. Wrinch and the present reviewer.

From statistical physics to statistical inference and back

TLDR
This work focuses on the development of Information Theory and its applications in Dynamical Systems, as well as Quantum Mechanics, where the role of information theory in quantum mechanics is concerned.

Guide to the Expression of Uncertainty in Measurement

6 Calculation using Monte Carlo simulation 9 6.1 Rationale and overview . . . . . . . . . . . . . . 9 6.2 The number of Monte Carlo trials . . . . . . 12 6.3 Sampling from probability distributions .

Frequentist ideas began in the early 1900's (see for example, Ref. 43 and references therein)

    Grunbegriffe der Messtechnick -Behandlung von Unsicherheiten bei der Auswertung von Messungen

    • DIN Deutsches Institut für Normung
    • 1985