Well, PhilGoetz is claiming (if I am finally understanding him) that casting things in the light of believe/disbelieve loses information. [...] We can't all be right...
I'm pretty sure both of us are right in this case. I agree that "casting things in the light of" believe/disbelieve can be unacceptably lossy. I was responding to you claiming it's a "weird thing to do" to infer a 55-85 interval based on common uses of the word "believe". Same word, but context seems to derive different concepts. AFAIK, people simply don't tend to use the word in the 55-85 sense when they're talking about "important" things (e.g., you don't often hear things in the tone of, "I believe global warming is a serious problem, let me get back to you on that").
However, I know that when I think to, I use the word "think" instead of "believe" because I think it's clearer, so on some level I must agree that "believe" leaves some sort of ambiguities.
In common usage, "think" and "believe" seem only to differ by degrees. For me, re-reading my above examples under s/believe/think/ seems to weaken the connoted confidence.
I was responding to you claiming it's a "weird thing to do" to infer a 55-85 interval based on common uses of the word "believe".
I thought I must be weird since I seem to have been the only one that completely didn't understand the post initially. But perhaps I just lack this other usage entirely, or perhaps I still don't agree. (See my response to Phil above: http://lesswrong.com/lw/10a/you_cant_believe_in_bayes/ssc)
...In common usage, "think" and "believe" seem only to differ by degrees. For me, re-reading my ab
Well, you can. It's just oxymoronic, or at least ironic. Because belief is contrary to the Bayesian paradigm.
You use Bayesian methods to choose an action. You have a set of observations, and assign probabilities to possible outcomes, and choose an action.
Belief in an outcome N means that you set p(N) ≈ 1 if p(N) > some threshold. It's a useful computational shortcut. But when you use it, you're not treating N in a Bayesian manner. When you categorize things into beliefs/nonbeliefs, and then act based on whether you believe N or not, you are throwing away the information contained in the probability judgement, in order to save computation time. It is especially egregious if the threshold you use to categorize things into beliefs/nonbeliefs is relatively constant, rather than being a function of (expected value of N) / (expected value of not N).
If your neighbor took out fire insurance on his house, you wouldn't infer that he believed his house was going to burn down. And if he took his umbrella to work, you wouldn't (I hope) infer that he believed it was going to rain.
Yet when it comes to decisions on a national scale, people cast things in terms of belief. Do you believe North Korea will sell nuclear weapons to Syria? That's the wrong question when you're dealing with a country that has, let's say, a 20% chance of building weapons that will be used to level at least ten major US cities.
Or flash back to the 1990s, before there was a scientific consensus that global warming was real. People would often say, "I don't believe in global warming." And interviews with scientists tried to discern whether they did or did not believe in global warming.
It's the wrong question. The question is what steps are worth taking according to your assigned probabilities and expected-value computations.
A scientist doesn't have to believe in something to consider it worthy of study. Do you believe an asteroid will hit the Earth this century? Do you believe we can cure aging in your lifetime? Do you believe we will have a hard-takeoff singularity? If a low-probability outcome can have a high impact on expected utility, you've already gone wrong when you ask the question.