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Check out the first chapter of Jayne's probability theory. It's the clearest take down of the frequentist interpretations that you have and introduction to the Bayesian interpretation.

http://www.med.mcgill.ca/epidemiology/hanley/bios601/Gaussia...

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Thanks, I had a quick skim through it and it seems really helpful. If I understand correctly, the claim is that the laws of probability as they are known comprise the only possible interpretation that satisfies the 3 desiderata set forth in chapter 1.

I don't remember, the thing which really helped me click at least the bayesian interpretation was if we have A --> B and B, then A is more plausible and probability reasoning is a way to quantify how more plausible A is now that we know B is true.

Chapter 5 is also a doozy in terms of explaining some of the things going on currently.

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