The Objective Bayesian Probability that an Unknown Positive Real Variable Is Greater Than a Known Is 1/2

• Published in: Philosophies (Basel) Vol. 6; no. 1; p. 24
• Main Authors: Fiorillo, Christopher D., Kim, Sunil L.
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.03.2021
• Subjects: Bayesian brain; inference; Jeffreys prior; minimal information; non-informative prior; Objectivity; prediction; Probability; Random variables; Robots; Sensors

If there are two dependent positive real variables x1 and x2, and only x1 is known, what is the probability that x2 is larger versus smaller than x1? There is no uniquely correct answer according to “frequentist” and “subjective Bayesian” definitions of probability. Here we derive the answer given t...