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

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Extended Form of Bayes Theorem 2

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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

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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%

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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%

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Doctors 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?

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Conditional Probabilities 9

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Prevalence in Population 10

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Bayes Theorem in Action 11

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Bayes Theorem in Action 12

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

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