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This seems like a good place to ask about something that I'm intensely curious about but haven't yet seen discussed formally. I've wanted to ask about it before, but I figured it's probably an obvious and well-discussed subject that I just haven't gotten to yet. (I only know the very basics of Bayesian thinking, I haven't read more than about 1/5 of the sequences so far, and I don't yet know calculus or advanced math of any type. So there are an awful lot of well-discussed LW-type subjects that I haven't gotten to yet.)
I've long conceived of Bayesian belief statements in the following (somewhat fuzzily conceived) way: Imagine a graph where the x-axis represents our probability estimate for a given statement being true and the y-axis represents our certainty that our probability estimate is correct. So if, for example, we estimate a probability of .6 for a given statement to be true but we're only mildly certain of that estimate, then our belief graph would probably look like a shallow bell curve centered on the .6 mark of the x-axis. If we were much more certain of our estimate then the bell curve would be much steeper.
I usually think of the height of the curve at any given point as representing how likely I think it is that I'll discover evidence that will change my belief. So for a low bell curve centered on .6, I think of that as meaning that I'd currently assign the belief a probability of around .6 but I also consider it likely that I'll discover evidence (if I look for it) that can change my opinion significantly in any direction.
I've found this way of thinking to be quite useful. Is this a well-known concept? What is it called and where can I find out more about it? Or is there something wrong with it?
I believe you may be confusing the "map of the map" for the "map".
If I understand correctly, you want to represent your beliefs about a simple yes/no statement. If that is correct, the appropriate distribution for your prior is Bernoulli. For a Bernoulli distribution, the X axis only has two possible values: True or False. The Bernoulli distribution will be your "map". It is fully described by the parameter "p"
If you want to represent your uncertainty about your uncertainty, you can place a hyperprior on p. This is y... (read more)