# Can a Jeffreys prior be used as an Information maximizing distribution if Information is defined using differential entropy?

I know that a Jeffreys prior is the information maximizing distribution for the statistical channel. However, I want to know if I define mutual information as $$I(x;y)=h(x)-h(x|y)$$ where $$h(.)$$ is differential entropy and $$x$$ and $$y$$ are continuous random variables. If I use $$p(x)$$ the PDF of $$x$$ to be the Jeffrey prior. Does $$h(x)=-\int p(x)log_2 p(x) dx$$ maximizes the $$I(x;y)$$?

• Related to Fisher information. Don't know if this can be related to Shannon entropy. Perhaps someone else does. – Carl Apr 11 at 5:44