tl;dr: Words are hard and people are horrible at being precise with them, even when doing or talking about math.
[epistemic status: maybe I’d want an actual textbook here but good enough] Looking into this, I have been grilling ChatGPT about what exactly a “belief” is in Bayesian Probability. According to it (from what I could gather), belief is a specific kind of probability. So a belief is just a number between 0 and 1 representing a probablity, but we use the label “belief” in specific contexts only. A prediction specifically is the pair of (statement about the future, belief). So a belief is not a prediction. Except when it is. I ask for examples and ChatGPT also loves going pars pro toto and belief is used synonymously with prediction a lot. And I’ve picked up the habit myself from reading here, before I ever learnt about the math at calculation level.
Personally, I dislike pars pro toto as I find that it makes things very confusing. So I will stop using the term “belief” to be synonymous with “prediction” from now on. Except when I won’t, because I suspect that it’s kind of convenient and sounds kind of neat.
tl;dr: Words are hard and people are horrible at being precise with them, even when doing or talking about math.
[epistemic status: maybe I’d want an actual textbook here but good enough]
Looking into this, I have been grilling ChatGPT about what exactly a “belief” is in Bayesian Probability. According to it (from what I could gather), belief is a specific kind of probability. So a belief is just a number between 0 and 1 representing a probablity, but we use the label “belief” in specific contexts only. A prediction specifically is the pair of (statement about the future, belief). So a belief is not a prediction. Except when it is. I ask for examples and ChatGPT also loves going pars pro toto and belief is used synonymously with prediction a lot. And I’ve picked up the habit myself from reading here, before I ever learnt about the math at calculation level.
Personally, I dislike pars pro toto as I find that it makes things very confusing. So I will stop using the term “belief” to be synonymous with “prediction” from now on. Except when I won’t, because I suspect that it’s kind of convenient and sounds kind of neat.
source: https://chat.openai.com/share/03a62839-3efc-483d-bebd-4cefa9064dfd