Original link	http://yamlb.wordpress.com/2006/04/12/interpretation-of-probability/
Date	2006-04-12
Status	publish

To understand the debate between frequencists and bayesian, I read about the philosophy of the probability concept. The problem is deeper than just the common debate. After reading the very interesting article from Plato Encyclopedia, I wrote this not-so-short note.

According to this article, there are several main interpretations:

Classical probabilities - based on the principle of indifference.
Logical probabilities - notion of "degree of implication" in a formal language.
Frequency interpretation - limiting relative frequencies in an hypothetical infinite sequence of trials.
Propensity - quality of the physical word. It represents an intrinsec tendency to behave in a certain way.
Subjective interpretation - degree of belief of a suitable agent.

Conclusion: Probability theory and its statistical aspects play a special role in science, mainly because they are a necessary tool to understand and interact with the complex real world. When using probabilities to speak about experiments, one has to provide a meaning, a physical interpretation of this concept. Depending on this interpretation, he should use the theory in different ways, for instance by assigning probabilities to different kind of objects. Despite the fact that all interpretations face some difficulties, bayesianism proposes a paradox-free, intuitive, consistent and rational methods for inference in a variety of practical cases. Moreover, bayesianism is a promising approach to understand quantum mechanics, rational decision making, psychology, and more generally, it has been presented as an extension of Aristotle’s logic

Comments

author: Pierre
date: 2006-07-10 14:26:22

Related material:

Probability, Causality and the Empirical World: A Bayes–de Finetti–Popper–Borel Synthesis A. P. Dawid

http://www.ucl.ac.uk/Stats/research/Resrprts/psfiles/STS088.pdf