bayes - Bayes’ Rule Bayes’ Rule - Updating...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Bayes’ Rule Bayes’ Rule - Updating Probabilities • Let A 1 ,…, A k be a set of events that partition a sample space such that (mutually exclusive and exhaustive): – each set has known P(A i ) > 0 (each event can occur) – for any 2 sets A i and A j , P(A i and A j ) = 0 (events are disjoint) – P(A 1 ) + … + P(A k ) = 1 (each outcome belongs to one of events) • If C is an event such that – 0 < P(C) < 1 ( C can occur, but will not necessarily occur) – We know the probability will occur given each event A i : P(C|A i ) • Then we can compute probability of A i given C occurred: ) ( ) and ( ) ( ) | ( ) ( ) | ( ) ( ) | ( ) | ( 1 1 C P C A P A P A C P A P A C P A P A C P C A P i k k i i i = + + = Example - OJ Simpson Trial • Given Information on Blood Test (T+/T-) – Sensitivity: P(T+|Guilty)=1 – Specificity: P(T-|Innocent)=.9957 ⇒ P(T+|I)=.0043 • Suppose you have a prior belief of guilt: P(G)=p* • What is “posterior” probability of guilt after seeing evidence that blood matches: P(G|T+)? 0043 . * 9957 . * ) 0043 *)(. 1 ( ) 1 ( * ) 1 ( * ) ( ) | ( ) ( ) ( ) ( ) | ( ) 0043 *)(. 1 ( ) 1 ( * ) | ( ) ( ) | ( ) ( ) ( ) ( ) ( + =- + = = =- + = = + = + = + + + + + + + + + + p p p p p T P G T P G P T P G T P T G P p p I T P I P G T P G P I T P G T...
View Full Document

This note was uploaded on 06/04/2011 for the course STA 4321 taught by Professor Staff during the Spring '08 term at University of Florida.

Page1 / 9

bayes - Bayes’ Rule Bayes’ Rule - Updating...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online