April08 - Agenda Tue 08 Apr Medical diagnostic test applications reasoning Using Bayess theorem probability formula Agenda Most of Rest Term Reasonings

# April08 - Agenda Tue 08 Apr Medical diagnostic test...

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Agenda Tue 08 Apr Medical diagnostic test applications reasoning Using Bayes’s theorem probability formula

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Agenda Most of Rest Term Reasonings often with hidden parts Eg generalization, survey type reasoning Eg science hypothesis testing type reasoning Eg reasoning using Bayes’s probability theorem
Example 2 HIV Problem Expt

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Problem 2 Reasoning Analyzed Premise1 Background: Risk group patient Premise2 Background: Error rate info for HIV test. Premise3: Patient has test. Test says "HIV+ . Correct conclusion?: • Chance (Patient HIV+) =95%?
Agenda Tue 08 Apr Medical diagnostic test applications reasoning Using Bayes’s theorem probability formula

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Bayes’s Theorem Hayes Online
Formula and Tree slide7 n cases H1 or H2 _________ H1 _________ H2 _________ E AND H1 Rate(H1) Rate(E | H1) Rate(H2) Rate(Not_E | H1) Rate(E | H2) Rate(Not_E | H2) _________ Not-E AND H1 _________ E AND H2 _________ Not_E AND H2 A B Posterior-rate(H1 | E) = E AND H1 / (E AND H1 + E AND H2)

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Agenda Most of Rest Term Reasonings often with hidden parts Eg generalization, survey type reasoning Eg science hypothesis testing type reasoning Eg reasoning using Bayes’s probability theorem
Problem 2 Reasoning Analyzed Premise1 Background: Risk group patient Premise2 Background: Error rate info for HIV test. Premise3: Patient has test. Test says "HIV+ . Correct conclusion?: Chance (Patient HIV+) =95%?

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Bayes Theorem Reasoning
Example 2 HIV Problem Expt

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Agenda Most of Rest Term Reasonings often with hidden parts Eg generalization, survey type reasoning Eg science hypothesis testing type reasoning Eg reasoning using Bayes’s probability theorem
Slide 13 Parts Science Investigation Part of real world (population, aspect) Hypotheses about part real world Data (sample, aspect) Research study design Inference about sample Conclusion about part real world

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Scientific Investigations Parts GRM 12.5 1. Understanding the problem. Scientists begin with a problem or question that presents itself during the examination of some data or phenomena. The problem may be generated by industry or by government, or it may arise in the speculative atmosphere of the laboratory. 2. Formulating a hypothesis. The next step involves the formulation of a hypothesis. These are proposed as solutions to a problem or as explanations for some strange or unexpected phenomenon. There may be a number of competing hypotheses, each offering a solution to or explanation of the problem. 3. Deducing the implications of the hypothesis. Having selected the most plausible hypothesis, the scientists' next step is to determine what observable consequences would have to follow if it were correct. Such inferences often take the form 'If h is the case, then x would have to occur under such and such conditions.' 4. Testing the hypothesis. Once the scientists have deduced what consequences should follow if the hypothesis is correct, they can devise and conduct tests to ascertain whether these consequences do indeed follow. The tests should be designed to
• Spring '11
• Leslie
• Null hypothesis, HIV+

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