All of Axion's Comments + Replies

Bayesian theorem is just one of many mathematical equations, like for example Pythagorean theorem. There is inherently nothing magical about it. It just happens to explain one problem with the current scientific publishing process: neglecting base rates. Which sometimes seems like this: "I designed an experiment that would prove a false hypothesis only with probability p = 0.05. My experiment has succeeded. Please publish my paper in your journal!" (I guess I am exaggerating a bit here, but many people 'doing science' would not understand immediately what is wrong with this. And that would be those who even bother to calculate the p-value. Not everyone who is employed as a scientist is necessarily good at math. Many people get paid for doing bad science.) This kind of thinking has the following problem: Even if you invent hundred completely stupid hypotheses; if you design experiments that would prove a false hypothesis only with p = 0.05, that means five of them would be proved by the experiment. If you show someone else all hundred experiments together, they may understand what is wrong. But you are more likely to send only the successful five ones to the journal, aren't you? -- But how exactly is the journal supposed to react to this? Should they ask: "Did you do many other experiments, even ones completely irrelevant to this specific hypothesis? Because, you know, that somehow undermines the credibility of this one." The current scientific publishing process has a bias. Bayesian theorem explains it. We care about science, and we care about science being done correctly.

You are not alone in thinking the use of Bayes is overblown. It can;t be wrong, of course, but it can be impractical to use and in many real life situations we might not have specific enough knowledge to be able to use it. In fact, that's probably one of the biggest criticisms of lesswrong.

Regarding Bayes, you might like my essay on the topic, especially if you have statistical training.

I know a few answers to this question, and I'm sure there are others. (As an aside, these foundational questions are, in my opinion, really important to ask and answer.) 1. What separates scientific thought and mysticism is that scientists are okay with mystery. If you can stand to not know what something is, to be confused, then after careful observation and thought you might have a better idea of what it is and have a bit more clarity. Bayes is the quantitative heart of the qualitative approach of tracking many hypotheses and checking how concordant they are with reality, and thus should feature heavily in a modern epistemic approach. The more precisely and accurately you can deal with uncertainty, the better off you are in an uncertain world. 2. What separates Bayes and the "traditional scientific method" (using scare quotes to signify that I'm highlighting a negative impression of it) is that the TSM is a method for avoiding bad beliefs but Bayes is a method for finding the best available beliefs. In many uncertain situations, you can use Bayes but you can't use the TSM (or it would be too costly to do so), but the TSM doesn't give any predictions in those cases! 3. Use of Bayes focuses attention on base rates, alternate hypotheses, and likelihood ratios, which people often ignore (replacing the first with maxent, the second with yes/no thinking, and the latter with likelihoods). 4. I honestly don't think the quantitative aspect of priors and updating is that important, compared to the search for a 'complete' hypothesis set and the search for cheap experiments that have high likelihood ratios (little bets). I think that the qualitative side of Bayes is super important but don't think we've found a good way to communicate it yet. That's an active area of research, though, and in particular I'd love to hear your thoughts on those four answers.