# Lesson 27 - Module 10 Reasoning with Uncertainty...

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Module 10 Reasoning with Uncertainty - Probabilistic reasoning Version 1 CSE IIT, Kharagpur

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Lesson 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=+ve|D=true) * P(D=true) P(D=true|T=+ve) = ------------------------------------------------------------ P(T=+ve|D=true) * P(D=true)+ P(T=+ve|D=false) * P(D=false) Version 1 CSE IIT, Kharagpur

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0.95 * 0.01
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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.

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Lesson 27 - Module 10 Reasoning with Uncertainty...

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