What is the mathematical difference between using a un-informative prior and a frequentist approach? Un-informative priors are preferred in instances where bias is not acceptable (ie. courtrooms, etc.)
However, it seems to me that it would just make sense to use a frequentist approach instead. Why does the Bayesian approach even have a non-informative prior?
Thanks!
 A: Even with a non-informative prior, Bayesian inference is different from frequentist approaches.  For example, consider estimating the probability $\theta$ that a coin will turn up heads.  Take a uniform prior on $\theta$.  If we observe a single flip, and it is heads, the Bayesian predictive probability that the next flip will be heads is 2/3.  A maximum-likelihood approach would say the probability is 1.  If you want the derivation of this result, read Bayesian inference, entropy, and the multinomial distribution.
I have written several papers on exactly this topic.  If you want more examples, check out:  Pathologies of Orthodox Statistics, Inferring a Gaussian distribution and Bayesian inference of a uniform distribution.  
A: It's for methodological purists who cannot bear to use boring 'ol frequentist stats with all their "horrible" inconsistencies (forget the fact that uninformative priors are often improper!).
Seriously, though: An uninformed Bayesian posterior distribution will look an awful lot like a normalized likelihood function, whereas a frequentist would report the usual confidence interval. Since frequentist inference does not obey the likelihood "principle", the two answers may be quite different.
