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Module
10
Reasoning with
Uncertainty 
Probabilistic reasoning
Version 1 CSE IIT, Kharagpur
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27
Probabilistic Inference
Version 1 CSE IIT, Kharagpur
10.4 Probabilistic Inference Rules
Two rules in probability theory are important for inferencing, namely, the product rule
and the Bayes' rule.
Here is a simple example, of application of Bayes' rule.
Suppose you have been tested positive for a disease; what is the probability that you
actually have the disease?
It depends on the accuracy and sensitivity of the test, and on the background (
prior
)
probability of the disease.
Let P(Test=+ve  Disease=true) = 0.95, so the false negative rate,
P(Test=ve  Disease=true), is 5%.
Let P(Test=+ve  Disease=false) = 0.05, so the false positive rate is also 5%.
Suppose the disease is rare: P(Disease=true) = 0.01 (1%).
Let D denote Disease and "T=+ve" denote the positive Tes.
Then,
P(T=+veD=true) * P(D=true)
P(D=trueT=+ve) = 
P(T=+veD=true) * P(D=true)+ P(T=+veD=false) * P(D=false)
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This note was uploaded on 09/20/2010 for the course MCA DEPART 501 taught by Professor Hemant during the Fall '10 term at Institute of Computer Technology College.
 Fall '10
 hemant

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