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 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.
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 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.