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Bayes and Prejudice: Overcoming Human Probability Errors

Discover the common errors in human probability judgment and how they lead to prejudice. Learn how applying Bayes' Theorem can rectify these mistakes and eliminate biases in decision-making processes. Through practical examples like Pitbulls and profiling, explore the importance of understanding base rates and avoiding stereotyping. This presentation challenges the reliance on misleading statistics and highlights the significance of implementing Bayesian principles in everyday scenarios to enhance critical thinking skills.

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Bayes and Prejudice: Overcoming Human Probability Errors

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  1. Bayes and Prejudice Detlof von Winterfeldt Professor of Industrial and Systems Engineering Professor of Public Policy Director, Center for Risk and Economic Analysis of Terroris Events University of Southern California EURO 2016 Poznan, Poland July 4, 2016

  2. Two Fundamental Errors in Human Probability Judgment • Equating P(H|D) with P(D|H) • 90% of all CEOs of all Fortune 500 companies (CEO) had a pet when they were young (Pet) • P(Pet|CEO) = 0.90 • P(Pet|Not CEO) = 0.90 • Ignoring base rates • Taxicab problem • P(HIV|positive RAPID test)

  3. Reverend Bayes to the Rescue

  4. Bayes’ Theorem or in odds-liklihood ratio form

  5. Takeaway Points of this Presentation • These errors are common • They contribute to prejudice • Using Bayes theorem can fix these errors • We should find simple ways to eliminate them!

  6. Pitbulls and Profiling (Courtesy of Malcolm Gladwell, The New Yorker, 2007)

  7. Would You Pet this Dog?

  8. Let’s Look at the Data: Fatal Attacks by Dog Breed

  9. Number of Fatal Dog Attacks (1979-1998)

  10. A Simple Calculation • P(Pitbull|Attack) = 0.32 • P(Attack|Pitbull)= P(Pitbull|Attack)*P(Attack)/P(Pitbull) = ? • Inputs: • Attacks = 238/20years = 11.9/year • Number of dogs: 80 million/year • P(Attack) = 11.9/80m = 1.49*10-7 • P(Pitbull) = 0.05 (about 4 million pitbulls) • Answer = 0.32*1.49*10-7/0.05 ~ 10-6 • About the same as dying in a plane crash in 1 RT

  11. Venn Diagram of Pitbull Attacks 80 million Dogs ~12 Fatal Attacks ~4 4 million Pitbulls Pitbull  Fatal Attack

  12. Non-Breed Factors • Gender (male) • Reproductive state (not neutered) • Dog size • Dog’s past behavior • Owner behavior (trains agression; neglects; chains) • Owner not present during attack • Victim (defenseless or elderly)

  13. A Terrorism Example Recent Announcement at Washington Dulles Airport: “Will Muhammed Ramzi, Ali Azhar, and Abdullah Saliba please proceed immediately to boarding gate 84 – Your plane to Munich is about to leave”

  14. What Do We Know? • Three men with Arab names • Traveling from DC to Munich • Late for the flight ________________________________ P(Terrorists|Arab Names) = ???

  15. Application to Terrorists All Passengers 150 Million People With Arab Name Terrorists Terrorists  Arab Name

  16. What To Do? • Find more important and more powerful distinguishing categories • Age • Watch lists • Travel indicators • Past criminal record • Behavioral indicators ____________________________________ Given these indicators, the name or ethnicity may not add much relevant information

  17. Scientists Make Similar Mistakes • “Childred with childhood leukemia are 20% more likely to live near high-voltage power lines than those that don’t” • Should a family with two children worry about buying a house near a powerline? • P(Childhood Leukemia) ~ 1 in 10,000 • 20% increases this to 1.2 in 10,000 • Survival rate is 90%

  18. Takeaway Points of this Presentation • These errors are common • Made by laypeople and experts • Provide more dramatic reports of statistical findings • They contribute to prejudice • Used by people who pander to prejudice • Provide drama and “human interest” to journalists • Using Bayes’ Theorem can fix these errors • Should we teach Bayes’ Theorem in elementary school? • We should find simple ways to eliminate these errors • Venn diagrams with simple counts? • Similar approached by Gigerenzer and Hastie and Dawes

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