Equipossibility is a philosophical concept in possibility theory that is a precursor to the notion of equiprobability in probability theory. It is used to distinguish what can occur in a probability experiment. For example, it is the difference between viewing the possible results of rolling a six sided dice as {1,2,3,4,5,6} rather than {6, not 6}.[1] The former (equipossible) set contains equally possible alternatives, while the latter does not because there are five times as many alternatives inherent in 'not 6' as in 6. This is true even if the die is biased so that 6 and 'not 6' are equally likely to occur (equiprobability).
The Principle of Indifference of Laplace states that equipossible alternatives may be accorded equal probabilities if nothing more is known about the underlying probability distribution. However, it is a matter of contention whether the concept of equipossibility, also called equispecificity (from equispecific), can truly be distinguished from the concept of equiprobability.[2]
^"Socrates and Berkeley Scholars Web Hosting Services Have Been Retired | Web Platform Services". web.berkeley.edu. Retrieved 2022-05-29.
^Wright, J. N. (January 1951). "Book Reviews". The Philosophical Quarterly. 1 (2): 179–180.
^Jensen, A.; la Cour-Harbo, A. (2001). "The Discrete Wavelet Transform via Lifting". Ripples in Mathematics. Berlin, Heidelberg: Springer. pp. 11–24.
External linksedit
Book Chapter by Henry E. Kyburg Jr. on equipossibility, with the 6/not-6 example above
Quotes on equipossibility in classical probability
April 14, 2024
equipossibility, philosophical, concept, possibility, theory, that, precursor, notion, equiprobability, probability, theory, used, distinguish, what, occur, probability, experiment, example, difference, between, viewing, possible, results, rolling, sided, dice. Equipossibility is a philosophical concept in possibility theory that is a precursor to the notion of equiprobability in probability theory It is used to distinguish what can occur in a probability experiment For example it is the difference between viewing the possible results of rolling a six sided dice as 1 2 3 4 5 6 rather than 6 not 6 1 The former equipossible set contains equally possible alternatives while the latter does not because there are five times as many alternatives inherent in not 6 as in 6 This is true even if the die is biased so that 6 and not 6 are equally likely to occur equiprobability The Principle of Indifference of Laplace states that equipossible alternatives may be accorded equal probabilities if nothing more is known about the underlying probability distribution However it is a matter of contention whether the concept of equipossibility also called equispecificity from equispecific can truly be distinguished from the concept of equiprobability 2 In Bayesian inference one definition of equipossibility is a transformation group which leaves invariant one s state of knowledge Equiprobability is then defined by normalizing the Haar measure of this symmetry group 3 This is known as the principle of transformation groups References edit Socrates and Berkeley Scholars Web Hosting Services Have Been Retired Web Platform Services web berkeley edu Retrieved 2022 05 29 Wright J N January 1951 Book Reviews The Philosophical Quarterly 1 2 179 180 Jensen A la Cour Harbo A 2001 The Discrete Wavelet Transform via Lifting Ripples in Mathematics Berlin Heidelberg Springer pp 11 24 External links editBook Chapter by Henry E Kyburg Jr on equipossibility with the 6 not 6 example above Quotes on equipossibility in classical probability Retrieved from https en wikipedia org w index php title Equipossibility amp oldid 1216083442, wikipedia, wiki, book, books, library,
