Editing Bayesian inference (section)

===Alternatives to Bayesian updating===
Bayesian updating is widely used and computationally convenient. However, it is not the only updating rule that might be considered rational.

[[Ian Hacking]] noted that traditional "[[Dutch book]]" arguments did not specify Bayesian updating: they left open the possibility that non-Bayesian updating rules could avoid Dutch books. Hacking wrote:<ref>{{cite journal |last=Hacking |first=Ian |date=December 1967 |page=316 |title=Slightly More Realistic Personal Probability |journal=Philosophy of Science |doi=10.1086/288169 |volume=34 |number=4 |s2cid=14344339}}</ref> "And neither the Dutch book argument nor any other in the personalist arsenal of proofs of the probability axioms entails the dynamic assumption. Not one entails Bayesianism. So the personalist requires the dynamic assumption to be Bayesian. It is true that in consistency a personalist could abandon the Bayesian model of learning from experience. Salt could lose its savour."

Indeed, there are non-Bayesian updating rules that also avoid Dutch books (as discussed in the literature on "[[probability kinematics]]") following the publication of [[Richard C.&nbsp;Jeffrey]]'s rule, which applies Bayes' rule to the case where the evidence itself is assigned a probability.<ref>{{cite web |url=http://plato.stanford.edu/entries/bayes-theorem/ |title=Bayes' Theorem (Stanford Encyclopedia of Philosophy) |publisher=Plato.stanford.edu |access-date=2014-01-05}}</ref> The additional hypotheses needed to uniquely require Bayesian updating have been deemed to be substantial, complicated, and unsatisfactory.<ref>[[Bas van Fraassen|van Fraassen, B.]] (1989) ''Laws and Symmetry'', Oxford University Press. {{ISBN|0-19-824860-1}}.</ref>