I've always been partial to Brad Efron's explanations, see http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.179.2128 http://citeseerx.ist.psu.edu/viewdoc

I've always been partial to Brad Efron's explanations, see http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.179.2128 http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.179.... IMO he nails the key distinction here: "One definition says that a frequentist is a Bayesian trying to do well, or at least not too badly, against any possible prior distribution." And there's some nice humor also: "The 250-year debate between Bayesians and frequentists is unusual among philosophical arguments in actually having important practical consequences."