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Lect16 - Course Logisics We need more TAs Or less work for...

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Course Logisics We need more TAs Or less work for Dae Hoon Grading is the time- consuming portion… Machine Problem?
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Religious wars among Statisticians (are you a Bayesian?) Frequentist / objectivist / classical statistics / Fisherian World is some true distribution Data are a random sampling We can come to know the World approximately via data Hypothesize; Observe; Evaluate Changing the hypothesis taints the data (baseball, lottery) Stock scam, wrong hypothesis Bayesian Evidence can be objective (data) or subjective Evidence can testify for / against different distributions Will my plane crash? Chance of rain? Two meter problem Two envelope problem
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Probability / Statistics Probability Space Sample space (Atomic Events) Event space Probability measure Random Variables Distributions Statistical Inference
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Joint Probability Distribution Discrete random variables Encodes all information of interest Allows arbitrary dependencies Exhaustive and Exclusive Atomic Events Must sum to 1 (one less degrees of freedom than entries) Diseases / Symptoms illustration (useful but overly specific; really evidence and conclusions)
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Sunny Cloudy Rainy Snowy Yes 0.25 0.15 0.05 0.13 No 0.05 0.1 0.25 0.02 Weather Have Fun? P(Rainy) = 0.05 + 0.25 = 0.3 P(Rainy | Sunny) = P(Rainy   Sunny) P( Sunny) = 0.3 / 0.7 0.43 P(Fun | Sunny) = P(Fun Sunny) P(Sunny) = 0.25 / 0.3 0.83 Do I prefer Sun or Snow? P(Fun | Snowy) = 0.13 / 0.15 0.87 So I prefer snow
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Bayes Theorem P(A | B) = Easy to rederive (you should never get it wrong!) P(A B) = P(A | B) P(B) = P(B | A) P(A) Equate and solve for P(A | B) P(B | A) P(A) P(B)
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