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Unformatted text preview: es depend on underlying
disease probability distribution
I
Tx V(I) U V(U) W V(W) Modeling treatment Utilities:
improved: 5000 unchanged: 2500 worse: 5000 Modeling test: transfemoral arteriography How large is the tree? • Infinite, or at least (27+3+8)^(27+3+8), ~10^60 • What can we do?
– Assume any action is done only once
– Order:
• questions
• tests
• treatments • 27! x 4 x 3 x 2 x 8, ~10^30
• Search, with a myopic evaluation function
– like gametree search; what’s the static evaluator? – Measure of certainty in the probability distribution How many questions needed? • How many items can you distinguish by
asking 20 (binary) questions? 2^20
• How many questions do you need to ask to distinguish among n items? log2(n) • Entropy of a probability distribution is a
measure of how certainly the distribution
identifies a single answer; or how many
more questions are needed to identify it Entropy of a distribution For example:
H(.5, .5) = 1.0
H(.1, .9) = 0.47
H(.01, .99) = 0.08
H(.001, .999) = 0.01
H(.33, .33, .33) = 1.58 (!) H(.005, .455, .5) = 1.04 H(.005, .995, 0) = 0.045
(!)  should use logn P j Interacting with ARF in 1973 Question 1: What is the patient's age? 1 010 2 1130 3 3150 4 5170 5 Over 70 Reply: 5 The current distribution is:
Disease
Probability
FARF 0.58
IBSTR 0.22
ATN
0.09
Question 2: What is the patient's sex? 1 Male 2 Pregnant Female 3 Nonpregnant Female Reply: 1 . . . ARF in 1994 Local Sensitivity Analysis Casespecific Likelihood Ratios Therapy Planning Based on Utilities Assumptions in ARF • Exhaustive, mutually exclusive set of
diseases
• Conditional independence of all questions,
tests, and treatments
• Cumulative (additive) disutilities of tests
and treatments
• Questions have no modeled disutility, but
we choose to minimize the number asked
anyway...
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 Fall '10
 PeterSzolovits

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