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Emile 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.
The bayesian/frequentist distinction can cover three different things that may occasionally be mixed up:
The core philosophical disagreement (the "proper" one) about whether probabilities an agent's knowledge / uncertainty about the world, or whether they represent frequencies of some event. For example, a frequentist in this sense might say that it's meaningless to talk about the probability that the millionth binary digit of pi is even or odd. I think frequentist epistemology is mostly discredited, but that it used to be dominant.
There are a bunch of hodge-podge statistical methods and tests (like p-values); and later on attempts to unify everything in terms of bayesian methods. People used to the "old" methods may not particularly call themselves "frequentists" or care that much about such labels; those pushing for the new (better) methods are the ones stressing the distinction (hunting down the sin of frequentism), sometimes to the annoyance of the rest.
Thinking in probabilities versus thinking in frequencies (80 women out of a hundred); the human brain works better when a problem is presented in terms of frequencies