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PhilipL comments on Open Thread, October 16-31, 2012 - Less Wrong
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hello, all. first post around here =^.^= I've been working my way through the core sequences, slowly but surely, and I ran into a question I couldn't solve on my own. please note that this question is probably the stupidest in the universe.
what is the difference between the Bayesian and Frequentist points of view?
let me clarify: in Eli Yudkowsky's explanation of Bayes' theorem, he presented an iconic problem:
to my understanding of the Bayesian perspective, the answer would be 7.8% and would represent the degree of uncertainty that the subject has breast cancer
to my understanding of the Frequentist perspective, the answer would be 7.8% and would represent the frequency of subjects that both have cancer and tested positive.
a keen observer will understand where my confusion comes from- on my way through the core sequences, I have heard much from the Bayesian side, but nothing from the Frequentist side, making it seem artificially non-existent.
I had the same issue, and I'm personally not convinced there's an actual "Bayesian vs frequentist" conflict as framed in the sequences. Both are useful ways of thinking in different scenarios.
To use Emile's example, there's a distinction between the probability that you think the millionth digit of pi is even or odd, and whether it really is even or odd. Even though you don't know the millionth digit offhand, it can be computed and has a definite value, so it really doesn't matter what you think it is. Saying 50:50, or more generally an equal probability distribution, is in my mind basically the same as saying "I don't know" (i.e. "I have zero evidence for deciding one way or the other.")
There's also a difference between the parity of the millionth digit of pi, and, for example, the wind speed at an arbitrary place and future time. It's impossible to calculate, so instead you can apply Bayesian methods and estimate a range of values based on prior knowledge, and any historical data you might have access to.