Are there any areas of study that you feel are underrepresented here, and would be interesting and useful to lesswrongers?
I feel some topics are getting old (Omega, drama about moderation policy, a newcomer telling us our lack of admiration for his ideas is proof of groupthink, Friendly AI, Cryonics, Epistemic vs. Instrumental Rationality, lamenting how we're a bunch of self-centered nerds, etc. ...), and with a bit of luck, we might have some lurkers that are knowledgeable about interesting areas, and didn't think they could contribute.
Please stick to one topic per comment, so that highly-upvoted topics stand out more clearly.
I want to do an applied Bayesian analysis of what credence I should give to the Sierpinski conjecture being true.
I've been thinking that perhaps the small covering set sizes for known Sierpinski numbers, and the projections on where we expect to find primes (see A61) is enough to be "effectively certain" of the conjecture's truth even without actually having the prime counter-examples in hand. For instance, I feel like I should be able to quantify the value of Bayesian evidence that each primality test contributes to the overall project goal of proving the Sierpinski conjecture. And if I can show that I expect to update in favour of the conjecture's truth after hearing of the results of X more primality tests, then I should also be able to update on that now, right?
Working this out for a problem I'm familiar with might help us get better at analysing the truth of other scientific conjectures in general. But the reason I haven't done this so far is that despite understanding Bayesian reasoning abstractly and the rules about conserving probability, I don't know how to formally select a prior for the analysis. I realise this is probably not a big problem as long as it's not pathologically bad -- can I just say 50% true or maybe 90% since someone smart who I respect went to the trouble to publish a paper saying he believed it? Guess that's not hard, but how do I calculate the value of incremental evidence in favour of the conjecture's truth that has accumulated over the years as more and more possible ways for it to be false have been eliminated?
I picked this because I've been running the distributed computing system trying to solve this problem through brute-force computational means the past 8 years without actually knowing how sure I should be about the actual thing I'm trying to prove. It might be good to know what I'm doing, huh?