= 27d567bc2d48d9f40e9ccc20ea370b15)
radfordd comments on Probability is in the Mind - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (186)
Constant: The competent frequentist would presumably not be befuddled by these supposed paradoxes.
Not the last two paradoxes, no. But the first case given, the biased coin whose bias is not known, is indeed a classic example of the difference between Bayesians and frequentists. The frequentist says:
According to the frequentist, apparently there is no rational way to manage your uncertainty about a single flip of a coin of unknown bias, since whatever you do, someone else will be able to criticize your belief as "subjective" - such a devastating criticism that you may as well, um, flip a coin. Or consult a magic 8-ball.
Sudeep: If quantum mechanics is true, then ignorance/uncertainty is a part of nature and not just something that agents have.
A common misconception - Jaynes railed against that idea too, and he wasn't even equipped with the modern understanding of decoherence. In quantum mechanics, it's an objective fact that the blobs of amplitude making up reality sometimes split in two, and you can't predict what "you" will see, when that happens, because it is an objective fact that different versions of you will see different things. But all this is completely mechanical, causal, and deterministic - the splitting of observers just introduces an element of anthropic pseudo-uncertainty, if you happen to be one of those observers. The splitting is not inherently related to the act of measurement by a conscious agent, or any kind of agent; it happens just as much when a system is "measured" by a photon bouncing off and interacting with a rock.
There are other interpretations of quantum mechanics, but they don't make any sense. Making this fully clear will require more prerequisite posts first, though.
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 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".
yep.