A lot of the calculations (including the ability to use Bayes law) is common to Frequentists and Bayesians. Efron says the difference is Frequentists assume th

A lot of the calculations (including the ability to use Bayes law) is common to Frequentists and Bayesians. Efron says the difference is Frequentists assume the quantity to be modeled is unknown but has a single fixed value (so you can't make probability statements about it) and the measurements have some possible variability. Bayesians model the unknown with an explicit prior distribution for the unknown quantity to be inferred and assume the measurements are fixed. So each school means something different when they state a probability (Frequentist variation over data draws, Bayesian variation over the unknown to be measured). Gelman defines Bayesian methods as the proper setting up of a generative model and computing joint probabilities of parameters and data. In his view Frequentist don't compute joint probabilities but at best conditional probabilities (which assume out modeling likely values for the unknown quantity to be inferred). The joke of the comment is: both sides tend to snipe on the other (as neither framework looks good if you assume the other). My partner has a nice article on the topic: http://www.win-vector.com/blog/2013/05/bayesian-and-frequentist-approaches-ask-the-right-question/ http://www.win-vector.com/blog/2013/05/bayesian-and-frequent...