Bayes rule using higher order prior probability

[AltCtrlDel]

Hi

I am asking, if I am trying to make inference using Bayes rule based on a prior probability that is a random variable by itself; is it sufficient to use the expected value of such probability or there are other details.

Thanks in advance.

 

[winterfors]

It depends on what analysis you want to perform on the resulting posterior probability distribution.

If you are only interested in its expectation (or some other linear function of the posterior), you can use the expected value of the prior.

If you also want to calculate some nonlinear measure of the posterior (e.g. its variance) you need to compute all possible posteriors given all possible priors, calculate their respective variances, and then take the expectation of those.

Best wishes,

-Emanuel