Frequentist theory of probability

[Alan Grayson]

How can the frequentist theory of probability be applied to a system, such as the H atom, which has an infinite set of possible outcomes for all energy level transitions?  AG

[Jesse Mazer]

There are a number of variants of frequentism, would you include hypothetical frequentism with a time-ordering? Namely, the idea that probability should be understood in terms of a hypothetical scenario where we could do an unending number of trials, such that if the frequency of some outcome in the first N trials is f_N (with 'first N' defined in terms of the time they occurred, not some other ordering), then the probability of that outcome would be defined as the limit of f_N as N approaches infinity. In this case I don't see why an infinite set of possible outcomes should be a problem--if each outcome has some finite probability, that means the number of trials with that specific outcome approaches infinity in the limit as the total number of trials approaches infinity, and the relative frequencies of any given pair of outcomes should approach the ratio of their probabilities according to QM laws.

On Sun, Dec 4, 2022 at 11:24 PM Alan Grayson <agrays...@gmail.com> wrote:

How can the frequentist theory of probability be applied to a system, such as the H atom, which has an infinite set of possible outcomes for all energy level transitions?  AG

--
You received this message because you are subscribed to the Google Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email to everything-li...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/3de79f33-363c-4e00-aa0c-350432de25e6n%40googlegroups.com.

[Brent Meeker]

Right.  And frequentist interpretation is in fact applied in testing probabilistic theories like QM because in fact we can only have finite experimental results.

Brent

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAPCWU3J8Sq9vdHPJi7WqNT%2Bh4pW70JeMbFaxsveAjW0j8guryg%40mail.gmail.com.

[Lawrence Crowell]

Basically frequentism says there is some preexisting distribution of probabilities, a sample space, that once understood can predict all probabilities. This is an "objectivist" perspective. Bayesian statistics says for practical work this does not exist, we must use what limited knowledge we have to make an estimate, a Bayesian prior, and then compute a probability outcome. This can be repeated in a regression. In the end for N --> infinity frequentism and Bayesianism effectively converge to the same result.

LC