The logic that helped crack the Nazi Enigma code What is Bayesian logic? And Bayesian statistics? How does the theory work? Once you understand what it is, you’ll spot Bayesian reasoning in science, medicine - and many aspects of daily life. Sir David Spiegelhalter, Emeritus Professor of Statistics at the University of Cambridge, explains all. Made in partnership with @royalsocietyscience #BBCIdeas #EnigmaCode #Science #Medicine #Stats

You probably don't realise it, but every time you change your mind based on new information, like rethinking a decision after hearing a friend's advice, you're using something called Bayesian reasoning. Bayesian reasoning was first articulated by the Reverend Thomas Bayes, a clergyman from Tumberidge Wells in southern England way back in the 18th century. Thomas Bayes introduced two vital ideas. First, that our beliefs can be expressed as probabilities. And second, how our beliefs should be revised when we obtain more information. Alan Turing and his team at Bletchley Park used Bayesian ideas to learn about the settings of enigma machines in World War II, changing their opinion as new patterns were found. The spam filter on your email account will use Bayesian analysis to change its probability that your email message is spam as each new suspicious feature is detected. Fundamentally, Bayesian ideas reflect what it means to be human. We live in a world of uncertainty, but we always have prior expectations of what might happen next, and we revise that uncertainty as we learn from experience. All based on the ideas of a rather obscure 18th century cleric from Tom Bridge Wells.