# Uninformative (flat) Prior density for non-linear functions [duplicate]

We, bayesians, usually use non-informative priors for the parameters like

$p(\beta)\propto 1$.

Someone told me that such a flat prior is informative to some extent for non-linear functions of the parameters $\beta$. I thought this sort of prior was always uninformative for any kind of functional form.

I would appreciate some clarification on this point!

## marked as duplicate by Sean Easter, Michael Chernick, Peter Flom♦Jul 6 '17 at 10:42

For any function there are many ways we can reparameterize it, for example a normal distribution $N(0, \sigma^2)$ can be described by its standard deviation or by its variance. If you use a uniform prior over the standard deviation you get a different posterior compared to using a uniform prior over the variance. If you square a uniform variable you don't get another uniform variable.