The only sensible "non-informative" prior is Jeffreys' prior. Invariance under reparameterization of the parameter is what I would consider to be a non-negotiable feature of any non-informative prior belief.
To assign a (improper) uniform prior to the variance of a Gaussian distribution is to assign a non-uniform prior to its standard deviation, and vice versa. One can, in certain circumstances, assign priors to be non-inforamative in a particular way, but to be universally non-informative, no, it must be Jeffreys' or nothing at all.
In consideration of the aforementioned, the debate about non-informative Bayesian priors is a relic of 20th century philosophy. The construction of hiearchical causality networks for the purposes of unsupervised learning is the future of Bayesian statistics, and priors in this context are rarely non-informative.
To assign a (improper) uniform prior to the variance of a Gaussian distribution is to assign a non-uniform prior to its standard deviation, and vice versa. One can, in certain circumstances, assign priors to be non-inforamative in a particular way, but to be universally non-informative, no, it must be Jeffreys' or nothing at all.
In consideration of the aforementioned, the debate about non-informative Bayesian priors is a relic of 20th century philosophy. The construction of hiearchical causality networks for the purposes of unsupervised learning is the future of Bayesian statistics, and priors in this context are rarely non-informative.