Lecture 4-Probability Slides

13 24 independence events a and b are independent i p

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Unformatted text preview: is P(D1=1 | sum is 4)? 1/3 24 Independence Events A and B are independent iff P (A, B ) = P (A)P (B ) What are the alternate forms? 25 Independence Events A and B are independent iff P (A, B ) = P (A)P (B ) What are the alternate forms? P (A) = P (A|B ) P (B ) = P (B |A) 26 Jochen Triesch’s famous pizza slide (modified from B. Warner) Free Pizza! Venn diagrams in Pizza form from B. Warner Statistical Independence: P(A,B) = P(A)P(B) or equivalently: P(A|B) = P(A) or equivalently: P(B|A) = P(B) Pick slice at random! What is P(pepperoni) ? What is P(mushroom) ? What is P(pepperoni | mushroom) ? What is P(mushroom | pepperoni) ? What is P(mushroom, pepperoni) ? 27 mushroom and pepperoni events are independent! 28 Conditional Independence Venn diagrams in Pizza form from B. Warner Conditional Independence: P(A,B|C) = P(A|C)P(B|C) Are the presence of mushrooms P(mushroom, anchovy | pepperoni): and anchovies x 1/5 NO! 1/5 = 3/5 independent given pepperoni P(mushroom, =epperoni | anchovy): 1/3 = 2/3 x 1/3 NO! P (M |P ) p ? P(anchovy, pepperoni | mushroom): 1/4 = 2/4 x 3/4 NO! Quiz: come up with pizza that has conditional independence Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch 12 29 Conditional Independence Venn diagrams in Pizza form from B. Warner Conditional Independence: P(A,B|C) = P(A|C)P(B|C) Are the presence of mushrooms P(mushroom, anchovy | pepperoni): and anchovies x 1/5 NO! 1/5 = 3/5 independent given pepperoni P(mushroom, =epperoni | anchovy): 1/3 = 2/3 x 1/3 NO! P (M |P ) p 3/5 P(anchovy, pepperoni | mushroom): 1/4 = 2/4 x 3/4 NO! Quiz: come up with pizza that has conditional independence Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch 12 30 Conditional Independence Venn diagrams in Pizza form from B. Warner Conditional Independence: P(A,B|C) = P(A|C)P(B|C) Are the presence of mushrooms P(mushroom, anchovy | pepperoni): and anchovies x 1/5 NO! 1/5 = 3/5 independent given pepperoni P(mushroom, =epperoniA|P ) = ? 1/3 = 2/3 x 1/3 NO! P (M |P ) p 3/5 P ( | anchovy): P(anchovy, pepperoni | mushroom): 1/4 = 2/4 x 3/4 NO! Quiz: come up with pizza that has conditional independence Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch 12 31 Conditional Independence Venn diagrams in Pizza form from B. Warner Conditional Independence: P(A,B|C) = P(A|C)P(B|C) Are the presence of mushrooms P(mushroom, anchovy | pepperoni): and anchovies x 1/5 NO! 1/5 = 3/5 independent given pepperoni P(mushroom, =epperoniA|P ) = 1/5 P (A, 1/3|P ) /3 ? 1/3 NO! P (M |P ) p 3/5 P ( | anchovy): M = 2= x P(anchovy, pepperoni | mushroom): 1/4 = 2/4 x 3/4 NO! Quiz: come up with pizza that has conditional independence Jochen Triesch, UC San Diego, http://cogsci.uc...
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This note was uploaded on 02/09/2014 for the course COGS 109 taught by Professor Staff during the Fall '08 term at UCSD.

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