Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 36 / 1 / a / Solution

If ${\pi }_0=\mathbb{P}(H_0)$ and ${\pi }_1=\mathbb{P}(H_1)=1-{\pi }_0$, the prior odds on the null hypothesis areThese odds concern which model is true before seeing the observations. They are separate from the prior distribution of the success probability within the alternative model.