Bayes' Theorem and Bayes' Theorem

[Longfellow]

After looking into it some more, it looks to me like there are two things that are called "Bayes' Theorem." One is an actual theorem in probability theory that has been proven mathematically under certain special conditions, and which is not what anyone is actually using in any field where it is allegedly being used, like medicine or weather forecasting. What people mean when they say that they are using Bayes' theorem is not actually a theorem. It's a formula in that theorem which would be obvious to anyone with 20 hours of training in probability, and which has been proven again and again to produce false results sometimes from inputs that everyone agrees are true, when it is not used in those special conditions.

(later) The special conditions are that the input numbers are taken from a probability space. "A probability space is a triple (Ω,𝔽,P)
where Ω is a sample space, 𝔽 is a sigma-algebra of events and P is a probability measure on 𝔽."

Probability space | Definition, axioms, explanation​

Discover the building blocks of a probabiliy space and read detailed explanations of the axioms that define them.

www.statlect.com

 

[Longfellow]

Even the actual theorem that no one is using hardly deserves to be called a theorem. It's like calling "distance = velocity x time" a "theorem." Just applying some algebra to a definition.

 

[Longfellow]

After reading and thinking about it some more, it looks to me like what people call "Bayesian statistics" doesn't actually contribute anything to the accuracy of predictions or judgments. The only reason for its popularity in some fields is that it streamlines decision making by allowing personal judgments to masquerade as results of statistical analysis.

 

[TheLightWithin]

After reading and thinking about it some more, it looks to me like what people call "Bayesian statistics" doesn't actually contribute anything to the accuracy of predictions or judgments. The only reason for its popularity in some fields is that it streamlines decision making by allowing personal judgments to masquerade as results of statistical analysis.

Good to know!

 

[Longfellow]

This turned up in my research into practical applications of the formula that is mislabeled "Bayes' Theorem."

Bayesian persuasion - Wikipedia

en.wikipedia.org

In economics and game theory, Bayesian persuasion occurs when one participant (the sender) wants to persuade the other (the receiver) of a certain course of action. There is an unknown state of the world, and the sender must commit to a decision of what information to disclose to the receiver. Upon seeing said information, the receiver will revise their belief about the state of the world using Bayes' Rule and select an action.

The applicability of the model has been assessed in a number of real-world contexts:
- Disclosure of capital reserves by banks to financial regulators.[13]
- Grading of students' work by teachers, where the receivers are potential future employers.[14]
- Provision of feedback by an employer to employees.[15]
- Revelation of plot points from a creator of fictional work to entertain its reader or viewer.