23:28 I don’t see how the fact that any finite sub-sequence of an infinite sequence has a zero weight in the infinite sequence’s average makes the reasoning behind applying the average back to the finite sample “unclear”. The idea is that we *assume* that every instance, e.g. every die throw or every coin flip, is a random variable that is independently and identically distributed, i.e. has exactly the same behavior and properties as any other instance of the same situation and can neither influence nor be influenced any other instance, whether past or future. Therefore, if there was any reason to expect from any one instance something different than what we would expect from an infinite sequence of such instances (occurring independently and identically distributed), then it would also be reasonable to expect the same from *every* other instance in the sequence, which would necessarily imply that the whole infinite sequence itself behaves differently than we first thought. The whole idea of repeating indefinitely the same experiment and calculating the frequencies is based on the assumption that we can truly perform that experiment time after time in an identical manner except for some aspects whose properties don’t change and which are precisely the source of variation. When we flip the same coin over and over, we assume that the coin itself doesn’t change much (e.g. doesn’t wear down) and that our different flips are not systematically (predictably) different.
I think we all agree that for a finite sampling, the outcomes won't necessarily equate to the infinite probabilities. For example, one roll of a dice will yield an integer from 1 through 6. The result of that one roll says nothing about the long-term probabilities (e.g., maybe the dice is "unfair"). As such, I think the speaker is saying that the usefulness of long-term probability figures don't necessarily help you for one (or a finite) number of rolls. For example, it would be remarkable if six rolls of a dice gave you exactly one 1, one 2, etc. In the end, I certainly agree with you (i.e., it's "smart" to assume 1/6 probabilty for X for one roll)... but unclear if that proves useful. But perhaps, I'm totally lost. Also, I thought he addressed your second point during the talk (i.e., he said something along the lines of you can't literally throw the same dice a "gazillion" times).
After a decade of of knowing probability, I finally got the intuition of it. You are awesome thank you very much. So logical, and clear and simple and concise and most importantly: ENTERTAINING =)
in fact there may only be subjective probability in that two observers will always have different levels of understanding the initial conditions and other factors affecting the outcome of an experiment.
When you compute summary statistics, such as mean and variance, of a probability distribution on the basis of empirical data, such as that on observed equity returns, you necessarily put each observation on an equal footing, implicitly assuming an objective view of probability. However, possibilities associated with return on equities are more like a degree of belief than frequency of occurrence in a series of trials in identical circumstances. To what extent is it valid to compute mean and variance of distribution of economic variables, the probability of realization of a particular realization of which is more like degree of belief than frequency of occurrence?
