Yes, odds notation is the only sane way to do Bayes. Who cares about Bayes theorem written out in math. Just think about hypotheses and likelihoods. If you need to rederive the math notation start from thinking in odds and rederive what you would do to get a probability out of odds.
I do sure feel confused why so many people mess up Bayes. The core of bayesian reasoning is literally just asking the question of “what is the probability that I would see this evidence given each one of my hypotheses”, or in the case of a reasonable null hypothesis and a hypothesized conjecture the question of “would I be seeing anything different if I was wrong/if this was just noise?”.
To be clear, this is also what is in all the standard Bayes guides. Eliezer’s Bayes guide both on Yudkowsky.net and Arbital.com is centrally about the odds notation.
Yes, odds notation is the only sane way to do Bayes. Who cares about Bayes theorem written out in math. Just think about hypotheses and likelihoods. If you need to rederive the math notation start from thinking in odds and rederive what you would do to get a probability out of odds.
I do sure feel confused why so many people mess up Bayes. The core of bayesian reasoning is literally just asking the question of “what is the probability that I would see this evidence given each one of my hypotheses”, or in the case of a reasonable null hypothesis and a hypothesized conjecture the question of “would I be seeing anything different if I was wrong/if this was just noise?”.
To be clear, this is also what is in all the standard Bayes guides. Eliezer’s Bayes guide both on Yudkowsky.net and Arbital.com is centrally about the odds notation.