Comment author:radfordd
18 May 2011 03:44:34PM
*
7 points
[-]

Eliezer:

"The coin's bias is not a random variable! It's a fixed fact! If you repeat the experiment, it won't come out to a 0.5 long-run frequency of heads!"

You're repeating the wrong experiment.

The correct experiment for a frequentist to repeat is one where a coin is chosen from a pool of biased coins, and tossed once. By repeating that experiment, you learn something about the average bias in the pool of coins. For a symmetrically biased pool, the frequency of heads would approach 0.5.

So your original premise is wrong. A frequentist approach requires a series of trials of the correct experiment. Neither the frequentist nor the Bayesian can rationally evaluate unknown probabilities. A better way to say that might be, "In my view, it's okay for both frequentists and Bayesians to say "I don't know.""

I think EY's example here should actually should be targeted at the probability as propensity theory of Von Mises (Richard, not Ludwig), not the frequentist theory, although even frequentists often conflate the two.

The probability for you is not some inherent propensity of the physical situation, because the coin will flip depending on how it is weighted and how hard it is flip. The randomness isn't in the physical situation, but in our limited knowledge of the physical situation.

The argument against frequentist thinking is that we're not interested in a long term frequency of an experiment. We want to know how to bet now. If you're only going to talk about long term frequencies of repeatable experiments, you're not that useful when I'm facing one con man with a biased coin.

That singular event is what it is. If you're going to argue that you have to find the right class of events in your head to sample from, you're already halfway down the road to bayesianism. Now you just have to notice that the class of events is different for the con man than it is for you, because of your differing states of knowledge, you'll make it all the way there.

Notice how you thought up a symmetrically biased pool. Where did that pool come from? Aren't you really just injecting a prior on the physical characteristics into your frequentist analysis?

If you push frequentism past the usual frequentist limitations (physical propensity, repeated experiments), you eventually recreate bayesianism. "Inside every Non-bayesian, there is a bayesian struggling to get out".

I think EY's example here should actually should be targeted at the probability as propensity theory of Von Mises (Richard, not Ludwig), not the frequentist theory, although even frequentists often conflate the two.

## Comments (186)

Old*7 points [-]Eliezer:

You're repeating the wrong experiment.

The correct experiment for a frequentist to repeat is one where a coin is chosen from a pool of biased coins, and tossed once. By repeating that experiment, you learn something about the average bias in the pool of coins. For a symmetrically biased pool, the frequency of heads would approach 0.5.

So your original premise is wrong. A frequentist approach requires a series of trials of the correct experiment. Neither the frequentist nor the Bayesian can rationally evaluate unknown probabilities. A better way to say that might be, "In my view, it's okay for both frequentists and Bayesians to say "I don't know.""

I think EY's example here should actually should be targeted at the probability as propensity theory of Von Mises (Richard, not Ludwig), not the frequentist theory, although even frequentists often conflate the two.

The probability for you is not some inherent propensity of the physical situation, because the coin will flip depending on how it is weighted and how hard it is flip. The randomness isn't in the physical situation, but in our limited knowledge of the physical situation.

The argument against frequentist thinking is that we're not interested in a long term frequency of an experiment. We want to know how to bet now. If you're only going to talk about long term frequencies of repeatable experiments, you're not that useful when I'm facing one con man with a biased coin.

That singular event is what it is. If you're going to argue that you have to find the right class of events

in your headto sample from, you're already halfway down the road to bayesianism. Now you just have to notice that the class of events is different for the con man than it is for you, because of your differing states of knowledge, you'll make it all the way there.Notice how you thought up a symmetrically biased pool. Where did that pool come from? Aren't you really just injecting a prior on the physical characteristics into your frequentist analysis?

If you push frequentism past the usual frequentist limitations (physical propensity, repeated experiments), you eventually recreate bayesianism. "Inside every Non-bayesian, there is a bayesian struggling to get out".

yep.