The Theory That Would Not Die: How Bayes' Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy cover
The Theory That Would Not Die: How Bayes' Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy
by Sharon Bertsch McGrayne
ISBN: 0300169698
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Symmetry · 2012-11-11 · Original thread
It's mostly a philosophical difference between thinking of probabilities as measures of relative frequency versus thinking of probabilities as measures about one's uncertainty about the outcome. There isn't so much a huge war between them as there used to be, but if you want to read about the history of that this was a book I enjoyed: http://www.amazon.com/The-Theory-That-Would-Not/dp/030016969...

Being horribly biased in favor of the Bayesian interpretation ever since I learned it was a thing I'll give an example of places that frequentists can be wrong. People who disagree can give counterexamples. ;)

http://lesswrong.com/lw/1gc/frequentist_statistics_are_frequ...

On the other hand, some argue that certain forms of inference are invalid and that it doesn't matter if they give the correct answer or not in practice because they're invalid. Calculus was attacked on this basis early on because many mathematicians thought that taking the limit of something as it approached 0 wasn't a thing you should be able to do.