what is a fractional bit? it's a bit with uncertainty.
For example, if you ask me a yes/no question and you know that half of the time I just answer randomly, and the other half I tell the truth, then my answer will contain 1/2 bits of information.
I'm thinking now about how you can compare the entropy of a prior and posterior distribution, and the difference will be the number of bits of information gained between them. I'm not sure if this is valid 🤔
if you believe that you have a 90% likelihood of winning a lottery, and then 100 of your friends lose and you use bayes rule to update your likelihood to 50%, did you just lose information
(I didn't actually do the calculation to see what bayes theorem tells us what the posterior likelihood would be I just took 50% for examples sake lmao)
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