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Thinking and Deciding

Thinking and Deciding

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CONCLUSION 135<br />

2. p(aids) =.0001, p(pos|aids) =.99, p(pos|no aids) =.01<br />

p(aids|pos) =<br />

3. p(aids) =.20, p(pos|aids) =.99, p(pos|no aids) =.01<br />

p(aids|pos) =<br />

(.99)(.0001)<br />

= .0098<br />

(.99)(.0001) + (.01)(.9999)<br />

(.99)(.20)<br />

= .96<br />

(.99)(.20) + (.01)(.80)<br />

The lesson here is that tests can be useful in at-risk groups but useless for screening (e.g., of medical<br />

personnel).<br />

4. p(guilt) =.80, p(match|guilt) =1.00, p(match|innocent) =.05<br />

p(guilt|match) =<br />

(1.00)(.80)<br />

= .988<br />

(1.00)(.80) + (.05)(.20)<br />

5. You know p(D|H0) =.0016, but you must make a judgment of the prior p(H1), which is the same<br />

as 1 − p(H0) <strong>and</strong> of p(D|H1). The latter depends on how big you judge the effect would be. Then<br />

p(H1|D) =<br />

p(D|H1)p(H1)<br />

p(D|H1)p(H1)+p(D|H0)p(H0) .<br />

The difficulty of specifying the unknown quantities helps us underst<strong>and</strong> why Bayesianism is unpopular<br />

among statisticians.

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