Inversion of Bayes’ Formula for Events
摘要
In standard notation, let { H 1, H 2, ⋯ , H m } and { A 1, A 2, ⋯ , A n } be two distinct partitions of the sample space, or equivalently two sets of events satisfying three properties: (i) each event is non-void, (ii) events in the same set are mutually exclusive (i.e. P( H j ∪ H k ) = P( H j ) + P( H k ) for j≠ k), and (iii) each set is collectively exhaustive, (i.e. \(P(\cup ^m_{i=1} H_j)=1\) ).