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P(EB)PriorsThe probability of our existing belief prior to the new evidence.
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P(EB | NE)=P(EB)xP(NE | EB)
P(NE | EB)
LiklihoodThe probability of the new evidence occuring assuming the existing belief is valid.Posterior Probability=PriorsxLiklihood
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P(NE)P(NE)New Evidence probThe probability of the new evidence occuring.
New Evidence
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P(EB | NE)
Posterior Probability
The probability of our existing belief but given the new evidence.
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34%=85%x40%
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100%
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Posterior Prob
Priors
Liklihood
NE Prob
ExampleNarrativeNotes
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50.0%1%99%2%1Rare disease affecting 1% of population and a test that is 95% accurate. If you test positive what is the chance you have the disease?1%1%
P(Disease) x P(Positive test | Disease) + P(NoDisease) x P(Positive test | NoDisease)
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50.0%25%100%50%2You draw a card from a deck and reveal it to the dealer. The dealer says it is red. What is the chance it is a diamond?
Priors - 25% chance card is a diamond. If it’s a diamond, there is a 100% chance it is red. Half (50%) of the cards are red)
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21.4%74%13%45%3You have 2 investment options, A and B. Prob Inv A has positive return is 74%. Prob Inv B has positive return is 45%. Prob of Inv A being positive WHEN Inv B is positive is 13%
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14.0%10%7%5%4What is the chance a patient has liver disease given they are an alcoholic? Clinic prior - 10% of people have liver disease. 5% of patients entering clinic are alcoholic. 7% of of patients with liver disease are alcoholics
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23.0%12%10%5%5What is the chance a US citizen commits a crime and is poor? What if 11.5% of americans fall below the poverty line? What if 5% of people commited a crime over the last year? What if 10% of people commiting crimes are poor?0.0038
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29.6%33%40%45%6Box A contains 2 Red Balls and 3 Black balls, Box B contains 3 Red Balls and 1 Black balls, Box C contains 1 Red Balls and 4 Black balls. All 3 Boxes have equal prob of being picked. As such, what is the prob that a red ball was picked from box A?P(A|Rb)Priors =
1/3 since there are only 3 boxes
P(Rb|A) =
0.4
New Evidence, evenly weighted (1/3)
Box A0.4Box B0.75Box C0.2
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34.0%=85%X40%/100%7Mia is 25. She was taught to "Never give up," "Winners never quit and Quitters never win," And, most important in a job is that hard work, performance , and perseverance will be rewarded." She is in her first job and a few of her co-workers got laid off. She has received excellent performance reviews but is concened about the company. She is considering leaving but her teaching from growing up are giving her the signal to stick to it. What should she do? What is the probability she should stay in her job and not seek to change?Priors =
90% is best guess from growing up that she should stay
(P(NE|EB)
Mia needs to figure out if the people that got laid off were because they were not good or because the company is having business trouble. After asking around, the company is having economic trouble, and she "heard" the people that got fired were good people. She is more certain about the companies troubles 70% and less certain about the laid off peoples' quailty. (35%) So, she averaged the two toget the liklihood , since they are affsetting conditions. They are affsetting because a company laying off means ones ability is not going to help if the company is struggling. On the otherhand, if one is hard working, performing, and persevering, then they will be most likely to be kept by the company.
The new evidence is 100%, people are getting laid off.
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