Here Arnold just repeats a very standard distinction in probability. Not sure what there is to talk about unless we want to repeat standard debates about which concept is better for what.
unless we want to repeat standard debates about which concept is better for what.
Well, yes. Eliezer has suggested that “The ancient war between the Bayesians and the accursèd frequentists stretches back through decades”, but Kilng’s post describes a class of problems for which he presents the frequentist approach as being the reasonable one. I had rather hoped for a discussion, even if it started “standard”.
The usual Bayesian position is that the Bayesian picture subsumes the frequentist one. In cases where there’s a clear single frequentist answer to the question “what’s P(X)?” the answer is typically the same for any Bayesian who doesn’t have a crazy prior. Likewise for instances where you can get the answer “axiomatically”.
So, with Kling’s first example, everyone agrees: modulo quibbling about the usual idealizations, the probability is 1⁄2. An accursed frequentist might say that the Bayesian apparatus is unnecessary or confusing when asking this question; a Bayesian might say that saying simply “the probability is 1/2” (without any mention of what you’re conditioning on) is setting oneself up for confusion when subtleties arise later; but working out the probability that a fair coin, fairly tossed, comes up heads is not an instance where anyone thinks Bayesians get the wrong answer.
With Kling’s second example, I think even the most hardened (and accursed) frequentist would agree that “what is the probability that X happens?” and “what fraction of the time has X happened in the past?” are not the same question. Frequentism isn’t the idea that you always answer probability questions by looking at historical data. It’s the idea that what statements about probability mean are about long-term averages—historical and future. Here, again, I don’t think Kling has given an example where the frequentist approach is “the reasonable one”; I’m not sure he’s even given an example where the frequentist approach is a reasonable one.
It seems to me that to call that third probability “purely subjective” is unhelpful. Compare a statement to which applying that label is more obviously reasonable: “Beethoven’s third symphony is better than his fifth”. It’s not clear that there’s even any way to state that without using evaluative terms whose primary meaning is subjective. Whereas in principle, at least, one could estimate the probability Kling asks for in a way that even a frequentist might accept: do some sort of vast computer model of the world and run a big Monte Carlo simulation. Totally impractical, of course, but any question you could in principle answer that way surely isn’t purely subjective.
Quite possibly Kling does in fact have a decent grasp of this stuff, but I don’t see a great deal of insight in that page.
Here Arnold just repeats a very standard distinction in probability. Not sure what there is to talk about unless we want to repeat standard debates about which concept is better for what.
Well, yes. Eliezer has suggested that “The ancient war between the Bayesians and the accursèd frequentists stretches back through decades”, but Kilng’s post describes a class of problems for which he presents the frequentist approach as being the reasonable one. I had rather hoped for a discussion, even if it started “standard”.
The usual Bayesian position is that the Bayesian picture subsumes the frequentist one. In cases where there’s a clear single frequentist answer to the question “what’s P(X)?” the answer is typically the same for any Bayesian who doesn’t have a crazy prior. Likewise for instances where you can get the answer “axiomatically”.
So, with Kling’s first example, everyone agrees: modulo quibbling about the usual idealizations, the probability is 1⁄2. An accursed frequentist might say that the Bayesian apparatus is unnecessary or confusing when asking this question; a Bayesian might say that saying simply “the probability is 1/2” (without any mention of what you’re conditioning on) is setting oneself up for confusion when subtleties arise later; but working out the probability that a fair coin, fairly tossed, comes up heads is not an instance where anyone thinks Bayesians get the wrong answer.
With Kling’s second example, I think even the most hardened (and accursed) frequentist would agree that “what is the probability that X happens?” and “what fraction of the time has X happened in the past?” are not the same question. Frequentism isn’t the idea that you always answer probability questions by looking at historical data. It’s the idea that what statements about probability mean are about long-term averages—historical and future. Here, again, I don’t think Kling has given an example where the frequentist approach is “the reasonable one”; I’m not sure he’s even given an example where the frequentist approach is a reasonable one.
It seems to me that to call that third probability “purely subjective” is unhelpful. Compare a statement to which applying that label is more obviously reasonable: “Beethoven’s third symphony is better than his fifth”. It’s not clear that there’s even any way to state that without using evaluative terms whose primary meaning is subjective. Whereas in principle, at least, one could estimate the probability Kling asks for in a way that even a frequentist might accept: do some sort of vast computer model of the world and run a big Monte Carlo simulation. Totally impractical, of course, but any question you could in principle answer that way surely isn’t purely subjective.
Quite possibly Kling does in fact have a decent grasp of this stuff, but I don’t see a great deal of insight in that page.