We demonstrate the property of reparametrization invariance with a simple example on a Bernoulli statistical model. We start with the model \textsf{Ber}(q), which has parameter q. What is its Jeffreys prior? Express your answer as an un-normalized pdf \pi (q) in proportionality notation such that \pi (0.5)=2.

Question

\pi (q) \propto

Answer 1

\pi (q) \propto \sqrt{\frac{1}{q(1-q)}}