I wrote this out for myself in attempt to fully grasp this and maybe someone else might find it useful:
You have two theories, A and B. A is more complex then B, but has sharper/more precise predictions for it's observables.
i.e. given a test, where it's either +-ve or -ve (true or false), then we necessitate that P(+ | A) > P(+ | B).
Say that P(+ | A) : P(+ | B) = 10 : 1, a favorable likelihood ratio.
Then each successful +-ve test gives 10 : 1 odds for theory A over theory B.
You can penalize A initially for algorithmic complexity and estimate/assign i... (read more)
I wrote this out for myself in attempt to fully grasp this and maybe someone else might find it useful:
You have two theories, A and B. A is more complex then B, but has sharper/more precise predictions for it's observables. i.e. given a test, where it's either +-ve or -ve (true or false), then we necessitate that P(+ | A) > P(+ | B).
Say that P(+ | A) : P(+ | B) = 10 : 1, a favorable likelihood ratio.
Then each successful +-ve test gives 10 : 1 odds for theory A over theory B. You can penalize A initially for algorithmic complexity and estimate/assign i... (read more)