Ash Ch.2, continued. (We'll use Moore&McCabe section 4.5 with Ash 2.1 &2.4, review section 5.1 with Ash 2.3)
Bayes' theorem: Don't memorize the theorem, just know the
process.
From knowing an outcome D, find the probability of an antecedent
A.
P(A|D) when D|A is the direction
you have information for.
These can always be modeled effectively with a tree, A on the
first branhing, D on the second:
Find the probability of the outcome D by summing
the "fav" tree path results. (Ash's "total probability" p. 58)
Note the probability of A and D: just the single
path with A followed by D.
Divide: (AandD path) / (sum of D paths) = P(A
and D)/P(D) = P(A|D)
Reading : Bayes' theorem, Ash pp 58-61,
M&M pp 355-6. Handout case study: testing for AIDS.
ahead? Independence, M&M
pp.356-7, 292, 346 Rule 5. Ash pp. 41-43
HW Draw trees. Make a table if you think it adds
to your understanding.
Not Bayes, but interesting and useful: Moore&McCabe p. 369
4.111 Do this problem with x as the actual proportion
of plagiarism, y as the proportion who answer yes. Solve for
x in terms of y.
Handout: If not completed in class: #1 (lefthanded
families). Make a tree and a table, with all probabilities.
Moore&McCabe, p. 360 ff: Add to 4.88 from last time
4.90. Also 4.91 and 4.93. p. 369, 4.112 (& read Handout--the
probabilities are slightly different; the issues are the same.)
Ash sec. 2-1, p. 44
Add to 3a from last time: 3b.
4, 6
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