XAMPLE 2-38 Bayesian Network ayesian networks are used on the Web sites of high-technology manufacturers to allow customers to quickly diagnose problems with products. An versimplified example is presented here. A printer manufacturer obtained the following probabilities from a database of testresults. Printer failures are associated ith three types of problems: hardware, software, and other (such as connectors), with probabilities 0.1, 0.6, and 0.3, respectively. The probability of a printer lure given a hardware problem is 0.9, given a software problem is 0.2, and given any other type of problem is 0.5. If a customer enters the manufacturer's Web te to diagnose a printer failure, what is the most likely cause of the problem? et the events H, S, and O denote a hardware, software, or other problem, respectively, and let F denote a printer failure. The most likely cause of the problem is e one that corresponds to the largest of P(HIF), r(SIF), and P(OIF). In Bayes' Theorem the denominator is P(F) = P(F\H)P(H) + P(F|S)P(S) + P(F|O)P(0) = 0.9(0.1) + 0.2(0.6) + 0.5(0.3) = 0.36 hen, P(H|F) = P(F\H)P(H) / P(F) = 0.9(0.1) /0.36 = 0.250 P(SF) = P(F|S)P(S) / P(F) = 0.2(0.6) / 0.36 = 0.333 P(O|F) = P(F\O)P(O) I P(F) = 0.5(0.3) / 0.36 = 0.417 otice that P(HIF) + P(SIF) + P(OIF) = 1 because one of the three types of problems is responsible for the failure. Because P(OIF) is largest, the most likely cause the problem is in the other category. A Web site dialog to diagnose the problem quickly should start with a check into that type of problem. actical Interpretation: Such networks are more commonly used to diagnose problems in areas as diverse as electronic products and healthcare. The probability that a printer works if it has software problem. O The probability that software works if it has a printer problem. O The probability that a printer works and the software works. The probability that there is a software problem if the printer is working.
XAMPLE 2-38 Bayesian Network ayesian networks are used on the Web sites of high-technology manufacturers to allow customers to quickly diagnose problems with products. An versimplified example is presented here. A printer manufacturer obtained the following probabilities from a database of testresults. Printer failures are associated ith three types of problems: hardware, software, and other (such as connectors), with probabilities 0.1, 0.6, and 0.3, respectively. The probability of a printer lure given a hardware problem is 0.9, given a software problem is 0.2, and given any other type of problem is 0.5. If a customer enters the manufacturer's Web te to diagnose a printer failure, what is the most likely cause of the problem? et the events H, S, and O denote a hardware, software, or other problem, respectively, and let F denote a printer failure. The most likely cause of the problem is e one that corresponds to the largest of P(HIF), r(SIF), and P(OIF). In Bayes' Theorem the denominator is P(F) = P(F\H)P(H) + P(F|S)P(S) + P(F|O)P(0) = 0.9(0.1) + 0.2(0.6) + 0.5(0.3) = 0.36 hen, P(H|F) = P(F\H)P(H) / P(F) = 0.9(0.1) /0.36 = 0.250 P(SF) = P(F|S)P(S) / P(F) = 0.2(0.6) / 0.36 = 0.333 P(O|F) = P(F\O)P(O) I P(F) = 0.5(0.3) / 0.36 = 0.417 otice that P(HIF) + P(SIF) + P(OIF) = 1 because one of the three types of problems is responsible for the failure. Because P(OIF) is largest, the most likely cause the problem is in the other category. A Web site dialog to diagnose the problem quickly should start with a check into that type of problem. actical Interpretation: Such networks are more commonly used to diagnose problems in areas as diverse as electronic products and healthcare. The probability that a printer works if it has software problem. O The probability that software works if it has a printer problem. O The probability that a printer works and the software works. The probability that there is a software problem if the printer is working.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Transcribed Image Text:EXAMPLE 2-38 Bayesian Network
Bayesian networks are used on the Web sites of high-technology manufacturers to allow customers to quickly diagnose problems with products. An
oversimplified example is presented here. A printer manufacturer obtained the following probabilities from a database of test results. Printer failures are associated
vwith three types of problems: hardware, software, and other (such as connectors), with probabilities 0.1,0.6, and 0.3, respectively. The probability of a printer
failure given a hardware problem is 0.9, given a software problem is 0.2, and given any other type of problem is 0.5. If a customer enters the manufacturer's Web
site to diagnose a printer failure, what is the most likely cause of the problem?
Let the events H, S, and O denote a hardware, software, or other problem, respectively, and let F denote a printer failure. The most likely cause of the problem is
the one that coresponds to the largest of P(HIF), P(SIF), and P(OIF). In Bayes' Theorem the denominator is
P(F) = P(FH)P(H) + P(F|S)P(S) + P(F|O)P(O)
= 0.9(0.1) + 0.2(0.6) + 0.5(0.3) = 0.36
Then,
P(HF) = P(F|H)P(H)/ P(F) = 0.9(0.1)/0.36 = 0.250
P(SF) = P(F|S)P(S) / P(F) = 0.2(0.6) /0.36 = 0.333
P(OF) = P(F|0)P(O) I P(F) = 0.5(0.3) /0.36 = 0.417
Notice that P(HIF) + P(SIF) + P(OIF) = 1 because one of the three types of problems is responsible for the failure. Because P(OIF) is largest, the most likely cause
of the problem is in the other category. A Web site dialog to diagnose the problem quickly should start with a check into that type of problem.
Practical Interpretation: Such networks are more commonly used to diagnose problems in areas as diverse as electronic products and healthcare.
O The probability that a printer works if it has software problem.
O The probability that software works if it has a printer problem.
O The probability that a printer works and the software works.
O The probability that there is a software problem if the printer is working.
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