Open thread, Nov. 02 - Nov. 08, 2015

MrMind

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If it's worth saying, but not worth its own post (even in Discussion), then it goes here.

Notes for future OT posters:

1. Please add the 'open_thread' tag.

2. Check if there is an active Open Thread before posting a new one. (Immediately before; refresh the list-of-threads page before posting.)

3. Open Threads should be posted in Discussion, and not Main.

4. Open Threads should start on Monday, and end on Sunday.

Yes, I agree that people sometimes construct a box for themselves and then become terribly fearful of stepping outside this box (="this is impossible"). This does lead to them either not considering at all the out-of-the-box options or assigning, um, unreasonable probabilities to what might happen once you step out.

The problem, I feel, is that there is no generally-useful advice that can be given. Sometimes your box is genuinely constricting and you'd do much better by getting out. But sometimes the box is really the best place (at least at the moment) and getting out just means you become lunch. Or you wander in the desert hoping for a vision but getting a heatstroke instead.

You say

I don't think people take seriously the idea that taking negligible in-model probabilities seriously will pay off on net

but, well, should they? My "in-model probabilities" tell me that I'm not going to become rich by playing the lottery. Should I take the lottery idea seriously? Negligible probabilities are often (but not always) negligible for a good reason.

Given that, I am very hesitant to round p=epsilon down to p=0

Sure. But things have costs. If the costs (in time, effort, money, opportunity) are high enough, you don't care whether it's epsilon or a true zero, the proposal fails the cost-benefit test anyway.

but, well, should they?

Yes. From the inside it can be very tough to tell, but from the outside they're clearly they're wrong about them all being low probability. They don't check for potential problems with the model before trusting it without reservation, and that causes them to be wrong a lot. Even if your "might as well be 100%" is actually 97% - which is extremely generous, you'll be wrong about these things on a regular basis. It's a separate question of what - if anything - to do about it, but I'm not going to declare that I know there... (read more)