I'm pretty humble about what I know. That said, it sometimes pays to not undersell (when others are confidently wrong, and there's no time to explain why, for example).
I'm not so much talking about humility that you communicate to other people but about actually thinking that the other person might be right.
I don't see what "integral over many possibilities" has to do with consistency, except that it's sometimes the correct (but more expensive) thing to do.
There are cases where the forward backward algorithm gives you a path that's impossible to happen. I would call those paths inconsistent.
That's one of the lessons I learned in bioinformatics. Having a algorithm that robust to error is often much better than just picking the explanation that most likely to explain the data.
A map of the world that allows for some inconsistency is more robust than one where one error leads to a lot of bad updates to make the map consistent with the error.
I understand forward-backward (in general) pretty well and am not sure what application you're thinking of or what you mean by "a path that's impossible to happen". Anyway, yes, I agree that you shouldn't usually put 0 plausibility on views other than your current best guess.
r/Fitness does a weekly "Moronic Monday", a judgment-free thread where people can ask questions that they would ordinarily feel embarrassed for not knowing the answer to. I thought this seemed like a useful thing to have here - after all, the concepts discussed on LessWrong are probably at least a little harder to grasp than those of weightlifting. Plus, I have a few stupid questions of my own, so it doesn't seem unreasonable that other people might as well.