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 belie... (read more)

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)

0[anonymous]6yI 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 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 your "map of the map". Generally, people will use a beta distribution for this (rather than a bell-shaped normal distribution). With such a hyperprior, p is on the X-axis and ranges from 0 to 1. I am slightly confused about this part, but it is not clear to me that we gain much from having a "map of the map" in this situation, because no matter how uncertain you are about your beliefs, the hyperprior will imply a single expected value for p.
2Lumifer6yI don't understand where the bell curve is coming from. If you have one probability estimate for a given statement with some certainty about it, you would depict it as a single point on your graph. The bell curves in this context usually represent probability distributions. The width of that probability distribution reflects your uncertainty. If you're certain, the distribution is narrow and looks like a spike at the estimate value. If you're uncertain, the distribution is flat(ter). Probability distributions have to sum to 1 under the curve, so the smaller the width of the distribution, the higher the spike is. How likely you are to discover new evidence is neither here nor there. Even if you are very uncertain of your estimate, this does not convert into the probability of finding new evidence.

Open thread, 11-17 August 2014

by David_Gerard 1 min read11th Aug 2014274 comments

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