How to calculate the odds of something being true vs. it being false, given the evidence (Bayesian inference)

[Mauro]

But I thought total ignorance was expressed by 50%. "Between 100% and 0%" seems more correct — if there is no information, the probability is undefinable.

You really caught me on the spot there!

Well, I'm pretty sure the initial P(H), P(notH) probabilities should be set at 50% (and they are two trivial numbers anyway, we are at the stage of 'two hypothesis, absolutely zero evidence'). As for what to do when we have really zero knowledge when evaluating an evidence, by itself this is a pretty limit case, but must be solved if one wants to build a real working algorithm: it's not nice to get that 'division by zero' error. Being able to actually use Bayesian calculations in practice, with pen&paper or a PC, was actually the focus of my 'presentation', so this point was important for me. I used a fix which worked, but was nonetheless wrong, and of course I cannot certainly pretend to be able to debate with, say, a trained philosopher or mathematician on topics like this (I'm not that crazy! )

Oh well, having already revised my position about the 50%/50% a couple days ago (following your previous remark), I'd go for the venial sin, but fiat voluntas. All in all, it's just a technicality, but it should be fixed in the presentation (just I can't edit any more now).

But thanks a lot for having shown me a point where I first said one thing, then a totally different one. It was amazing, exhilarating (I'm serious)!

Sabine Hossenfelder has criticized other theoretical physicists for trying to calculate probabilities that we live in a multiverse, or that the anthropic principle explains fine-tuned parameters. Neither is possible, she says, because we can't inspect an ensemble of universes to learn how many belong to multiverses, or how many have parameters like ours. Otherwise I suppose it would be "50% probability that we live in a multiverse" or "50% probability that another random universe would have the same physical parameters" which doesn't seem useful.

I perfectly agree with you!!! I actually wrote the paragraph 'Chasing butterflies' (a wrong reasoning which looks to play on similar tunes to me, but I may be mistaken), and indeed the whole 'Pitfalls' chapter just to try to address that: you cannot use probabilities in absurd ways. I have probably failed in my intent, but I hope you'll agree with me that the why that reasoning you were referring to (the 50% multiverse etc.) does not work is not easy at all to explain in words. Indeed, I would very gladly hear an explanation (I'll look for Sabine Hossenfelder when I'll have the time I guess) so maybe I'll understand it better myself (then I'll only need the edit rights back).

Informationally, I don't see how one can go from ø to a specific number. Did you find a source?

I really can't figure out what your sentence means, sorry . If you mean that knowledge cannot be just conjured out of thin air, I perfectly agree with you! The whole matter of the 50%/50% probabilities was born out of the need to find an algorithmic way to say 'nothing in, nothing out', while the whole 'The tricky part' section tried to address 'garbage in, garbage out' (which is a much, much more difficult and significant problem, unfortunately).

Cheers!