E.T. Jaynes’ book is a pretty good resource: here are the first 3 chapters as pdf. Also see Savage’s alternate axiomization, which replaces the direct assumption of real numbers. The point from there is just that since the desiderata uniquely specify these rules, anything that bends the rules violates a desideratum. This leads to bad stuff, a claim which dutch book arguments are used to support.
Obviously you can’t always do the axiomatically correct thing and enumerate every single hypothesis (out to infinite length, but weighted inverse exponentially) to see which one is best supported by the data, so in the real world you approximate. Physical impossibility is the main flaw of using the complete Bayesian process :P
For the specific case of an artificial intelligence, Bayesianism is pretty much necessary because it talks about degrees of belief and probabilistic logic where frequentism doesn’t. If you instead need a mathematical tool to give you a feeling for how significant your results are, then frequentist and Bayesian textbooks will be pretty much equivalent. Though perhaps the Bayesian textbook will have better warnings about the problems with p-value significance tests.
E.T. Jaynes’ book is a pretty good resource: here are the first 3 chapters as pdf. Also see Savage’s alternate axiomization, which replaces the direct assumption of real numbers. The point from there is just that since the desiderata uniquely specify these rules, anything that bends the rules violates a desideratum. This leads to bad stuff, a claim which dutch book arguments are used to support.
Obviously you can’t always do the axiomatically correct thing and enumerate every single hypothesis (out to infinite length, but weighted inverse exponentially) to see which one is best supported by the data, so in the real world you approximate. Physical impossibility is the main flaw of using the complete Bayesian process :P
For the specific case of an artificial intelligence, Bayesianism is pretty much necessary because it talks about degrees of belief and probabilistic logic where frequentism doesn’t. If you instead need a mathematical tool to give you a feeling for how significant your results are, then frequentist and Bayesian textbooks will be pretty much equivalent. Though perhaps the Bayesian textbook will have better warnings about the problems with p-value significance tests.