Reasoning with Probs How does evidence lead to conclusions in situations of uncertainty? Bayes Theorem Data fusion, use of techniques that combine data from multiple sources and gather that information in order to achieve inferences, which will be more efficient and potentially more accurate than if they were achieved by means of a single source. Spam Cancer Screening Law Exams 1 ST2004 Week 7
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ST2004 Week 7 1
Reasoning with Probs
How does evidence lead to conclusions in situations of uncertainty? Bayes Theorem
Data fusion, use of techniques that combine data from multiple sources and gather that information in order to achieve inferences, which will be more efficient and potentially more accurate than if they were achieved by means of a single source.
SpamCancer ScreeningLawExams
ST2004 Week 7 2
Probability RulesConditional Prob and Independence
Important special Pr( ) Pr( | ) Pr( )
Pr( ) Pr( ) Prcase
( )
Aand B A B B
Aand B A B when independent
Multiplication Rule
All computed probs: depend on real world knowledgeassumptions about real world
Sometimes Useful to be explicitWhat - if
ST2004 Week 7 3
Exam Q from 2010
ST2004 Week 7 4
Brain Teasers• Two regular dice are rolled.
One is a 6. What’s the Pr (Other is 6) ? (Tijms, 8.1)
• Who is the murderer? (Tijms, Ch 1 Q6)?
Murder committed; know either X or Y – equally likely.Evidence: actual perp has blood group A
10% of people group A; X is group A Seek Pr( X is perp | evidence)
ST2004 Week 7 5
Brain Teasers
• Monty Hall Game Show (Tijms, Ch 1, Q11)
One car, behind one of three doors.Player selects one: say Door 1 Before opening this door
host opens one of two others: say Door 2 GOAT!host offers chance to change selection.
Metro Wed 10 Nov 2010Teens at risk from hyper-texting
Teenagers who send more than 100 text messages per day are more likely to have had sex, tried drugs, research has revealed.
4200 students at 20 schools; hyper-texting 19.2%Such teens 43% more likely to have tried alcohol.
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Serious
Sally Clarke - Sudden Infant Death SID The case was widely criticised because of the way statistical evidence was misrepresented in the original trial, particularly by Meadow. He stated in evidence as an expert witness that "one sudden infant death in a family is a tragedy, two is suspicious and three is murder unless proven otherwise" (Meadow's law).
He claimed that, for an affluent non-smoking family like the Clarks, the probability of a single cot death was 1 in 8,543, so the probability of two cot deaths in the same family was around "1 in 73 million" (8543 × 8543).
Sally Clarke - Sudden Infant Death SID He claimed that, for an affluent non-smoking family like the Clarks, the
probability of a single cot death was 1 in 8,543, so the probability of two cot deaths in the same family was around "1 in 73 million" (8543 × 8543).
218543Pr(2 Cot Deaths | Normal Family) = Pr(Normal Family | 2 Cot Deaths)
Pr(Normal | 2 Deaths) Pr(Normal ) Pr(2 Deaths | Normal)= Pr(Not normal | 2 Deaths) Pr(Not normal ) Pr(2 Deaths | Not normal)
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HomeWork• 2010 Exam Q• Discuss Metro• Tijms
– Q1, Ch 1 22 players + ref Friend bets €10 at least one common birthday
What is fair price of the bet
– Q12, Ch 1Told family has two children; one is a daughterProb other is daughter?Told family has two children; ring bell – girl opensProb other also a girl?
ST2004 Week 7 43
Spam Exam QA simple spam filter is used on a single incoming message. You know only a 1% chance of such messages are spam. You also know that the filter is imperfect - with false positive (ie positive for spam given not spam) and false negative rates of 5% and 2% respectively.
Defining events F± and S in a natural way, restate this information in terms