I'm given p(theta|y) equivalent to N(theta_hat,[I(theta_hat)]^{-1})
and I need to show this transformation:
[I(theta_hat)]^{1/2}(theta-theta_hat)|y ~ N(0,I)
where theta_hat is posterior mode and [I(theta_hat)]^{1/2} is any matrix square root of I(theta_hat).
Any ideas on how to show this? Thanks!