Solution

Past exam of the mathematics course of the University of Cambridge / 2008 / ii / Paper 4 / 27I / Solution

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

Past exam of the mathematics course of the University of Cambridge / 2024 / ib / Paper 3 / 18H / d / ii / Solution

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With a fixed diffuse alternative prior, a frequentist p-value and the posterior probability of a point null can order evidence differently. For $n=100$ and $\tau=1$, the p-value exceeds the null posterior near zero, while sufficiently far in the tails the null posterior exceeds the p-value because it has a slightly slower Gaussian decay.


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 Incoming links: Jeffreys-Lindley paradox for a Gaussian point null