In the wikipedia of "Student's t-distribution", "Bayesian inference" part, it is claimed that the prior distribution of the variance is taken to be
$p(\sigma^{2} \mid I) \propto 1/\sigma^{2}$
but I don't quite see why. This should come as a result of entropy maximization of the prior distribution but it is not obvious to me how this can be resulted.
Could you kindly help me on that?