INFORMATION THEORY BAYESIAN STATISTICS II Thomas Tiahrt, MA, PhD CSC492 – Advanced Text Analytics

Extended Form of Bayes Theorem 2

Extended Form Bayes Theorem 3

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Medical Tests 5  False positive  Test falsely indicates patient has disease  False negative  Test falsely indicates patient does not have disease

Medical Test Details 6  Disease tested for afflicts:5 of 1,000  When test returns a positive:  Rate of false positives:3%  Patient has disease :100%-3%=97%  When test returns a negative:  Rate of false negatives: 1%  Patient does not have disease: 100%-1%=99%

Medical Test Details 7  Disease tested for afflicts5 of 1,000  When test returns a positive:  Rate of false positives:3%  Patient has disease :100%-3%=97%  When test returns a negative:  Rate of false negatives: 1%  Patient does not have disease: 100%-1%=99%

Doctor’s Questions 8  Given a positive test:  What is the probability that a randomly chosen person actually has the disease?  Given a negative test:  What is the probability that a randomly chosen person does not have the disease?

Conditional Probabilities 9

Prevalence in Population 10

Bayes Theorem in Action 11

Bayes Theorem in Action 12

References 13 Sources: Foundations of Statistical Natural Language Processing, by Christopher Manning and Hinrich Schütze The MIT Press Fundamentals of Information Theory and Coding Design, by Roberto Togneri and Christopher J.S. deSilva Chapman & Hall / CRC

The end of part two of Bayesian statistics has come. End of PowerPoint 14