4 ms·
I'd say the justification is two parts. First is the Bernstein–von Mises theorem (priors don't matter once you have enough data, as long as you didn't violate
by jmount 12y ago
I'd say the justification is two parts. First is the Bernstein–von Mises theorem (priors don't matter once you have enough data, as long as you didn't violate Cromwell’s rule by using zeros). The second part is: improper priors are considered okay- as long as you check the posterior corresponds to a sensible distribution.
- Houshalter 12y agoIf I understand correctly, assuming all real numbers have equal prior probability, then no matter how much data you gather, it's still infinitely unlikely that the true value will exist within any finite range. E.g. the probability of the true value being between -100! and +100! is 0. If you draw from the distribution you will always draw "infinities".
- jmount 12y agoThat is why you have to check. If the P(data|param) is concentrated, then even for uniform priors on the real like you can have P(param|data) is proportional to a sensible distribution. But you have to check for specific model and data (say P(data|param) = c e^{(data-param)^2}), it isn't enough to verbally work through infinities.