Interpretation of Probability February 14, 2013 Thursday, February - - PowerPoint PPT Presentation

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Dec 22, 2023 215 likes •429 views

Interpretation of Probability February 14, 2013 Thursday, February 14, 13 Thursday, February 14, 13 Thursday, February 14, 13 Correlation is not causation Solution: Controlled experiments Thursday, February 14, 13 In 1999, UK prosecutors

SLIDE 1

Interpretation of Probability

February 14, 2013

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SLIDE 2

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Correlation is not causation Solution: Controlled experiments

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In 1999, UK prosecutors charged Sally Clark with murdering her two infant children, who had apparently both died in their sleep.

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Her defense: sudden infant death syndrome

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Expert witness: P(1 child dying of crib death) = 1/8550

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Expert witness: P(1 child dying of crib death) = 1/8550 P(both dying) = 1/8550^2 = 1/73 million

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The probability she is innocent is 1 in 73 million. Therefore, she must be guilty.

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The probability she is innocent is 1 in 73 million. Therefore, she must be guilty. What do you think?

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Error 1: P(innocent | both children dead) ≠ P(both children dead | innocent).

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Error 1: P(innocent | both children dead) ≠ P(both children dead | innocent). Error 2: No reason to believe the probabilities are

independent. (In fact, they likely aren’t:

susceptibility to SIDS is partly genetic.)

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Summary

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SLIDE 14

Risk = expected value of losses

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Risk = expected value of losses = P(loss) x amount of loss

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Choose the option where you’re likely to lose the least (i.e., smallest expected value of loss)

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Risk = expected value of losses = P(loss) x amount of loss

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Risk = expected value of losses = P(loss) x amount of loss

May be tricky

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SLIDE 19

Risk = expected value of losses = P(loss) x amount of loss

Need to use consistent units. Doesn’t take into account loss-aversion.

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