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If 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
by Houshalter 12y ago
If 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.