Uniform prior
= Uniform prior
A <uniform prior> on a finite-volume parameter region assigns constant <probability> density there and zero outside. On $[0,1]$ it is $\operatorname{Beta}(1,1)$, giving a <Beta distribution> posterior after <binomial distribution> data. Uniformity depends on the coordinate: a nonlinear reparametrization introduces a Jacobian and generally does not preserve a uniform density.