Editing Bayesian probability (section)

===Axiomatic approach===
[[Richard Threlkeld Cox|Richard T. Cox]] showed that Bayesian updating follows from several axioms, including two [[functional equations]] and a hypothesis of differentiability.<ref name = "vkdmsn" /><ref>{{cite book |first1=C. Ray |last1=Smith |first2=Gary |last2=Erickson |chapter=From Rationality and Consistency to Bayesian Probability |pages=29–44 |title=Maximum Entropy and Bayesian Methods |editor-first=John |editor-last=Skilling |location=Dordrecht |publisher=Kluwer |year=1989 |isbn=0-7923-0224-9 |doi=10.1007/978-94-015-7860-8_2 }}</ref> The assumption of differentiability or even continuity is controversial; Halpern found a counterexample based on his observation that the Boolean algebra of statements may be finite.<ref>{{cite journal |author=Halpern, J. |title=A counterexample to theorems of Cox and Fine |journal=Journal of Artificial Intelligence Research |volume=10 |pages=67–85|url=http://www.cs.cornell.edu/info/people/halpern/papers/cox.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.cs.cornell.edu/info/people/halpern/papers/cox.pdf |archive-date=2022-10-09 |url-status=live|doi=10.1613/jair.536 |year=1999 |s2cid=1538503 |doi-access=free }}</ref> Other axiomatizations have been suggested by various authors with the purpose of making the theory more rigorous.<ref name="rbp">{{cite journal |author1=Dupré, Maurice J. |author2=Tipler, Frank J. |url=http://projecteuclid.org/download/pdf_1/euclid.ba/1340369856 |title=New axioms for rigorous Bayesian probability |journal=Bayesian Analysis |volume=4 |year=2009 |issue=3 |pages=599–606|doi=10.1214/09-BA422 |citeseerx=10.1.1.612.3036 }}</ref>