You can also do Bayesian analysis with 'non-informative' priors or weakly-informative priors. As an example of the latter: if you're trying to figure out the mean change earth's surface temperature you might say 'it's almost certainly more then -50C and less than 50C'.
Unfortunately, if there is disagreement merely about how much prior uncertainty is appropriate, then this is sufficient to render the outcome controversial.
http://xkcd.com/1132/
Is this a fair representation of frequentists versus bayesians? I feel like every time the topic comes up, 'Bayesian statistics' is an applause light for me, and I'm not sure why I'm supposed to be applauding.