[wodenokoto]

You write that the frequentist doesn't answer the question, but it does. It answers

    P(H') = (H/H+T)^H'

You also write that the frequentist solution fails to give an error estimate, yet you don't show that the Bayesian solution does give one.

If the goal of the article is to show that Bayesian is more correct than frequentist then it leaves the reader unconvinced. If the goal is to show 3 ways of finding a probability, you should either say each is fine under its own paradigm, or argue why only one paradigm is correct.

[justinpombrio]

> You write that the frequentist doesn't answer the question, but it does. It answers > P(H') = (H/H+T)^H'

That's not the probability of getting H' heads in a row. It's an estimate of the probability of getting H' heads in a row based on a Maximum Likelihood estimation.

It doesn't make much sense if you take it to be the probability of getting H' heads in a row. For example, if {H=1, T=0}, then P(H'=100) = 1. You looked at one flip, and then decided that every subsequent flip was guaranteed to be heads?

It becomes even more clear that the question isn't really being answered if you take {H=0, T=0}.

[wodenokoto]

> That's not the probability of getting H' heads in a row. It's an estimate of the probability

Well, the true probability is unknown. You might assume a fair coin and do some Bayes rules, but how is that a guarantee of anything?

[justinpombrio]

> You might assume a fair coin and do some Bayes rules

Huh? Read the post, no one is assuming a fair coin.

[boostedsignal]

> You write that the frequentist doesn't answer the question, but it does. It answers: P(H') = (H/H+T)^H'

The question was asking for P(H' | H, T), not P(H').

> You also write that the frequentist solution fails to give an error estimate, yet you don't show that the Bayesian solution does give one.

Because there is no error? In the proof I assume P(p) is known and then after that every step follows from a law of probability. There is no error to be accounted for in the procedure. The only caveat is that we need to know P(p) to be able to perform the procedure, which is a caveat that I point out at least 3 times in the page.

[zAy0LfpBZLC8mAC]

> The only caveat is that we need to know P(p) to be able to perform the procedure

I think this is a very confusing way to put it. P(p) is not an objective value that you can know or not know, it is rather a model of our subjective knowledge, and therefore it doesn't really make sense to say "the caveat is that we need to know what our knowledge is" ... yeah, we do, but that is always the case by definition, so pointless to bring up.