Bayesian update

A Bayesian up­date or be­lief re­vi­sion is a change in prob­a­bil­is­tic be­liefs af­ter gain­ing new knowl­edge. For ex­am­ple, af­ter ob­serv­ing a pa­tient’s test re­sult, we might re­vise our prob­a­bil­ity that a pa­tient has a cer­tain dis­ease. If this be­lief re­vi­sion obeys Bayes’s Rule, then it is called Bayesian.

Bayesian be­lief up­dates have a num­ber of other in­ter­est­ing prop­er­ties, and ex­em­plify many key prin­ci­ples of clear rea­son­ing or ra­tio­nal­ity. Map­ping Bayes’s Rule onto real-life prob­lems of en­coun­ter­ing new ev­i­dence al­lows us to re­pro­duce many in­tu­itive fea­tures that have been sug­gested for “how to re­vise be­liefs in the face of new ev­i­dence”.

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  • Bayesian reasoning

    A prob­a­bil­ity-the­ory-based view of the world; a co­her­ent way of chang­ing prob­a­bil­is­tic be­liefs based on ev­i­dence.