Editing Principle of indifference (section)

==History==
This principle stems from [[Epicurus]]' principle of "multiple explanations" (pleonachos tropos),<ref>{{Cite book |last=Verde |first=Francesco |title=Lucretius Poet and Philosopher |chapter-url=https://www.degruyter.com/document/doi/10.1515/9783110673487-006/html |chapter=Epicurean Meteorology, Lucretius, and the Aetna |date=2020-07-06 |pages=83–102 |publisher=De Gruyter |isbn=978-3-11-067348-7 |language=en |doi=10.1515/9783110673487-006|s2cid=243676846 }}</ref> according to which "if more than one theory is consistent with the data, keep them all”. The epicurean [[Lucretius]] developed this point with an analogy of the multiple causes of death of a corpse.<ref>{{Cite journal |last1=Rathmanner |first1=Samuel |last2=Hutter |first2=Marcus |date=2011-06-03 |title=A Philosophical Treatise of Universal Induction |journal=Entropy |volume=13 |issue=6 |pages=1076–1136 |doi=10.3390/e13061076 |arxiv=1105.5721 |bibcode=2011Entrp..13.1076R |issn=1099-4300|doi-access=free }}</ref> The original writers on probability, primarily [[Jacob Bernoulli]] and [[Pierre Simon Laplace]], considered the principle of indifference to be intuitively obvious and did not even bother to give it a name. Laplace wrote:
:The theory of chance consists in reducing all the events of the same kind to a certain number of cases equally possible, that is to say, to such as we may be equally undecided about in regard to their existence, and in determining the number of cases favorable to the event whose probability is sought. The ratio of this number to that of all the cases possible is the measure of this probability, which is thus simply a fraction whose numerator is the number of favorable cases and whose denominator is the number of all the cases possible.

These earlier writers, Laplace in particular, naively generalized the principle of indifference to the case of continuous parameters, giving the so-called "uniform prior probability distribution", a function that is constant over all real numbers. He used this function to express a complete lack of knowledge as to the value of a parameter. According to Stigler (page 135), Laplace's assumption of uniform prior probabilities was not a meta-physical assumption.<ref>{{cite book |last= Stigler |first= Stephen M. |title= The History of Statistics: The Measurement of Uncertainty Before 1900 |publisher= Belknap Press of Harvard University Press |location= Cambridge, Mass |year= 1986 |isbn= 0-674-40340-1 |url=https://archive.org/details/historyofstatist00stig|url-access= registration }}</ref> It was an implicit assumption made for the ease of analysis.

The '''principle of insufficient reason''' was its first name, given to it by [[Johannes von Kries]],<ref>{{cite book |first1=Colin |last1=Howson |first2=Peter |last2=Urbach |chapter=Subjective Probability |pages=39–76 |title=Scientific Reasoning : The Bayesian Approach |location=La Salle |publisher=Open Court |year=1989 |isbn=0-8126-9084-2 }}</ref> possibly as a play on [[Gottfried Leibniz|Leibniz]]'s [[principle of sufficient reason]]. These later writers ([[George Boole]], [[John Venn]], and others) objected to the use of the uniform prior for two reasons. The first reason is that the constant function is not normalizable, and thus is not a proper probability distribution. The second reason is its inapplicability to continuous variables, as described above.

The "principle of insufficient reason" was renamed the "principle of indifference" by {{harvs|first=John Maynard|last=Keynes|authorlink=John Maynard Keynes|year=1921|txt}},<ref>{{cite book |last=Keynes |first=John Maynard |author-link=John Maynard Keynes |chapter=Chapter IV. The Principle of Indifference |title=A Treatise on Probability |volume=4 |publisher=Macmillan and Co. |year=1921 |chapter-url=https://books.google.com/books?id=YmCvAAAAIAAJ&pg=PA41 |pages=41–64|isbn=9780404145637 }}</ref> who was careful to note that it applies only when there is no knowledge indicating unequal probabilities.

Attempts to put the notion on firmer [[philosophy|philosophical]] ground have generally begun with the concept of [[equipossibility]] and progressed from it to [[equiprobability]].

The principle of indifference can be given a deeper logical justification by noting that equivalent states of knowledge should be assigned equivalent epistemic probabilities. This argument was propounded by [[Edwin Thompson Jaynes]]: it leads to two generalizations, namely the [[principle of transformation groups]] as in the [[Jeffreys prior]], and the [[principle of maximum entropy]].<ref>{{cite book |first=Edwin Thompson |last=Jaynes |title=Probability Theory: The Logic of Science |publisher=[[Cambridge University Press]] |year=2003 |isbn=0-521-59271-2 |chapter=Ignorance Priors and Transformation Groups |pages=327–347 |url=https://books.google.com/books?id=tTN4HuUNXjgC}}</ref>

More generally, one speaks of [[uninformative prior]]s.