What reparametrization of vector of parameters $\theta$ makes the Jeffreys prior $$\sqrt{\det I(\theta)}$$ correspond to the uniform prior?

A change of parametrization from $\theta$ to $\eta$ changes the Fisher information as follows (I think):

\begin{align} I(\eta) &= (\nabla_{\eta}{\theta}) I(\theta \mid X) {(\nabla_{\eta}{\theta})}^T \end{align}

E.g., for a Bernoulli distribution parametrized by probability $p\in[0,1]$, the Jeffreys prior is proportional to $\sqrt{\frac1{p(1-p)}}$. I believe the transformation in this case of

$$\eta = \int \sqrt{\frac1{p(1-p)}}\, dp = 2\arcsin(\sqrt{p})$$

has a uniform Jeffreys prior?

How do I generalize this to vector-valued values?


This is called the Variance-stabilizing transformation.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.