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Signal detection, conditional probability and Bayes’ theorem

Signal detection, conditional probability and Bayes’ theorem. Takashi Yamauchi TAMU. Given the data above, calculate d’, hit and false alarm. d’ = Hit= False alarm =. d’ = Z(Hit) – Z(False alarm) Hit= False alarm =. Definitions of hit and false alarm. Hit =

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Signal detection, conditional probability and Bayes’ theorem

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  1. Signal detection, conditional probability and Bayes’ theorem Takashi Yamauchi TAMU

  2. Given the data above, calculate d’, hit and false alarm. d’ = Hit= False alarm =

  3. d’ = Z(Hit) – Z(False alarm) Hit= False alarm =

  4. Definitions of hit and false alarm • Hit = P(resp = yes | stim = yes) • False alarm = P(resp = yes | stim = no)

  5. P(X | Y) = P(X, Y) / P(Y)

  6. Big Mac McDonald’s Diet Coke 100 Among all customers, how many of them bought Big Mac? Among all customers, how many of them bought Diet Coke? Among all customers, how many bought both Big Mac And Diet Coke? Among those bought Diet Coke, how many also bought Big Mac? 10 40 20 30

  7. Big Mac McDonald’s Diet Coke 100 • Among all customers, how many of them bought Big Mac? • P(Big Mac)=? • Among all customers, how many of them bought Diet Coke? • P(Diet Coke) =? • Among all customers, how many bought both Big Mac And Diet Coke? • P(Big Mac & Diet Coke) = ? • Among those bought Diet Coke, how many also bought Big Mac? • P(Big Mac | Diet Coke) =? 10 40 20 30

  8. P(Big Mac | Diet Coke) = P(Big Mac, Diet Coke) / P(Diet Coke) P(X | Y) = P(X, Y) / P(Y)

  9. McDonald’s 100 Big Mac 10 40 20 Diet Coke 30

  10. McDonald’s 100 Big Mac 10 40 20 Diet Coke 30

  11. McDonald’s 100 X 10 40 20 Y P(Y=yes)=? P(X=yes)=? P(Y=yes, X=yes)=? P(X=yes | Y=yes)=? 30

  12. 100 X Y 10 40 20 Hit =? P(resp=yes | stim = yes) False Alarm =? P(resp=yes | stim = no) 30

  13. Conditional probability P(X | Y) = P(X, Y) / P(Y) P(X| Y) P(Y) = P(X, Y) P(Y | X) = P(X, Y) / P(X) P(Y | X) P(X) = P(X, Y) Bayes’ theorem P(X | Y) P(Y) = P(Y | X) P(X) P(X | Y) = P(Y | X) P(X) / P(Y)

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