Interesting responses. Given that many of them miss the point, the point about a lack of examples is well taken. It is evidently impossible to communicate without using examples.
Now that's a hypothesis with only a bit of evidence and not much confidence, and the heuristic I'm getting at here would suggest that I really ought to consider collecting a wider sample. Maybe write 10 big comments randomly assigned to be exampleful or not exampleful, and see what actual correlations come up. Note that if I don't do that, I would have to think about subtle distinctions and effects, and many possibilities, but if I do, there's no room for such philosophy; the measurements would make it clear with little interpretation required.
And that forms our first example of what I'm trying to get at; when you form a hypothesis, it's a good idea to immediately think of whether there is an experiment that could disambiguate so far that you could think of it as a simple fact, or alternatively reveal your hypothesis as wrong. This is just the virtue of empiricism, which I previously didn't take seriously.
Maybe this is only useful to me due to my particular mental state before and after this idea, and because of the work I do. So here's some examples of the kind of stuff I had in mind to be clear:
Suppose you are designing a zinc-air alkaline fuel cell (as I am) and you see a funny degradation in the voltage over extended time, and a probe voltage wandering around. Preliminary investigations reveal (or do they?) that it's an ohmic (as opposed to electrochemical) effect in the current transfer parts. The only really serious hypothesis is that there is some kind of contact corrosion due to leaking. Great, we know what it is, let's rip it apart and rebuild it with some fix for that (solder). "No" says the Crush Your Uncertainty heuristic, "kick it when it's down, kill all other hypotheses, prove it beyond all suspicion."
So you do; you take it apart and painstakingly measure the resistance between all points and note the peculiar distribution of resistances very much characteristic to a corrosion issue in the one particular spot. But then oh look, the resistance depends on how hard you push on it (corrosion issue), the pins are corroded, and the contact surface has caustic electrolyte in it. And then while we're at it, we notice that the corrosion doesn't correlate with the leaks, and is basically everywhere conditional on any leak, because the nickel current distribution mesh wicks the electrolyte all over the place if it gets anywhere. And you learn a handful of other things (for example, why there are leaks, which was incidentally revealed in the thorough analysis of the contact issue).
...And we rip it apart and rebuild it with some solder. The decision at hand didn't change, but the information gained killed all uncertainty and enlightened us about other stuff.
So then imagine that you need lots of zinc in a particular processed form to feed your fuel cell, and the guys working that angle are debugging their system so there's never enough. In conversation it's revealed that you think there was 3 kg delivered, and they think they delivered 7. (For various reasons you can't directly measure it.) That's a pretty serious mistake. On closer analysis with better measurements next time, you both estimate ~12 kg. OK there's actually no problem; we can move on to other things. "No" says the Crush Your Uncertainty heuristic, "kick it when it's down." This time you don't listen.
...And it comes back to bite you. Turns out it was the "closer" inspection that was wrong (or was it?) Now its late in the game the CEO is looking for someone to blame, and there's some major problem that you would have revealed earlier if you'd listened to the CYU heuristic.
There's a bunch of others, mostly technical stuff from work. In everyday life I don't encounter enough of these problems to really illustrate this.
Again, this isn't really about Bayes vs Frequentism, it's about little evidence and lots of analysis vs lots of evidence and little analysis. Basically, data beats algorithms, and you should take that seriously in any kind of investigation.
Yeah. I work as a programmer, and it took me a while to learn even if you're smart, double-checking is so much better than guessing, in so many unexpected ways. Another lesson in the same vein is "write down everything".
Bayesian epistemology and decision theory provide a rigorous foundation for dealing with mixed or ambiguous evidence, uncertainty, and risky decisions. You can't always get the epistemic conditions that classical techniques like logic or maximum liklihood require, so this is seriously valuable. However, having internalized this new set of tools, it is easy to fall into the bad habit of failing to avoid situations where it is necessary to use them.
When I first saw the light of an epistemology based on probability theory, I tried to convince my father that the Bayesian answer to problems involving an unknown processes (eg. laplace's rule of succession), was superior to the classical (eg. maximum likelihood) answer. He resisted, with the following argument:
I added conditions (eg. what if there is no more evidence and you have to make a decision now?) until he grudgingly stopped fighting the hypothetical and agreed that the Bayesian framework was superior in some situations (months later, mind you).
I now realize that he was right to fight that hypothetical, and he was right that you should prefer classical max likelihood plus significance in most situations. But of course I had to learn this the hard way.
It is not always, or even often, possible to get overwhelming evidence. Sometimes you only have visibility into one part of a system. Sometimes further tests are expensive, and you need to decide now. Sometimes the decision is clear even without further information. The advanced methods can get you through such situations, so it's critical to know them, but that doesn't mean you can laugh in the face of uncertainty in general.
At work, I used to do a lot of what you might call "cowboy epistemology". I quite enjoyed drawing useful conclusions from minimal evidence and careful probability-literate analysis. Juggling multiple hypotheses and visualizing probability flows between them is just fun. This seems harmless, or even helpful, but it meant I didn't take gathering redundant data seriously enough. I now think you should systematically and completely crush your uncertainty at all opportunities. You should not be satisfied until exactly one hypothesis has non-negligible probability.
Why? If I'm investigating a system, and even though we are not completely clear on what's going on, the current data is enough to suggest a course of action, and value of information calculations say that decision is not likely enough to change to make further investigation worth it, why then should I go and do further investigation to pin down the details?
The first reason is the obvious one; stronger evidence can make up for human mistakes. While a lot can be said for it's power, human brain is not a precise instrument; sometimes you'll feel a little more confident, sometimes a little less. As you gather evidence towards a point where you feel you have enough, that random fluctuation can cause you to stop early. But this only suggests that you should have a small bias towards gathering a bit more evidence.
The second reason is that though you may be able to make the correct immediate decision, going into the future, that residual uncertainty will bite you back eventually. Eventually your habits and heuristics derived from the initial investigation will diverge from what's actually going on. You would not expect this in a perfect reasoner; they would always use their full uncertainty in all calculations, but again, the human brain is a blunt instrument, and likes to simplify things. What was once a nuanced probability distribution like
95% X, 5% Ymight slip to justXwhen you're not quite looking, and then, 5% of the time, something comes back from the grave to haunt you.The third reason is computational complexity. Inference with very high certainty is easy; it's often just simple direct math or clear intuitive visualizations. With a lot of uncertainty, on the other hand, you need to do your computation once for each of all (or some sample of) probable worlds, or you need to find a shortcut (eg analytic methods), which is only sometimes possible. This is an unavoidable problem for any bounded reasoner.
For example, you simply would not be able to design chips or computer programs if you could not treat transistors as infallible logical gates, and if you really really had to do so, the first thing you would do would be to build an error-correcting base system on top of which you could treat computation as approximately deterministic.
It is possible in small problems to manage uncertainty with advanced methods (eg. Bayes), and this is very much necessary while you decide how to get more certainty, but for unavoidable computational reasons, it is not sustainable in the long term, and must be a temporary condition.
If you take the habit of crushing your uncertainty, your model of situations can be much simpler and you won't have to deal with residual uncertainty from previous related investigations. Instead of many possible worlds and nuanced probability distributions to remember and gum up your thoughts, you can deal with simple, clear, unambiguous facts.
My previous cowboy-epistemologist self might have agreed with everything written here, but failed to really get that uncertainty is bad. Having just been empowered to deal with uncertainty properly, there was a tendency to not just be unafraid of uncertainty, but to think that it was OK, or even glorify it. What I'm trying to convey here is that that aesthetic is mistaken, and as silly as it feels to have to repeat something so elementary, uncertainty is to be avoided. More viscerally, uncertainty is uncool (unjustified confidence is even less cool, though.)
So what's this all got to do with my father's classical methods? I still very much recommend thinking in terms of probability theory when working on a problem; it is, after all, the best basis for epistemology that we know of, and is perfectly adequate as an intuitive framework. It's just that it's expensive, and in the epistemic state you really want to be in, that expense is redundant in the sense that you can just use some simpler method that converges to the Bayesian answer.
I could leave you with an overwhelming pile of examples, but I have no particular incentive to crush your uncertainty, so I'll just remind you to treat hypotheses like zombies; always double tap.