Throughout history, Bayesian methods have helped solve complex problems that were unsolvable by other means^1,2:

• During World War II, they were used to decode the German Enigma cipher and turn the tides of war
• The US Navy used them to search for a missing H-bomb and locate Soviet subs
• Insurance actuaries used them to set insurance rates
• They were used in court to demonstrate the innocence of Captain Dreyfus
• RAND corporation used them to assess the likelihood of a nuclear accident
• Harvard and Chicago researchers used them to verify the authorship of the Federalist Papers
• In medicine they were used to first establish the link between smoking and lung cancer

References:

1.      A History of Bayes’ Theorem

2.    McGrayne, S. The Theory That Would Not Die