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Exploring Dice Probabilities and Bayesian Formulas in Predictive Modeling

Dive into the world of dice probabilities, Bayesian formulas, and predictive modeling from medieval times to modern times. Learn about predictor variables, probability distributions, and how to make predictions based on prior and new data using logistic regression and Bayesian methods.

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Exploring Dice Probabilities and Bayesian Formulas in Predictive Modeling

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Presentation Transcript

  1. Overview • Probabilities • Probability Distribution • Predictor Variables • Prior Information • New Data • Prior and New Data

  2. Medieval Times: Dice and Gambling

  3. Modern Times: Dice and Games/Gambing

  4. Dice Probabilities 1 6 Dice Outcome are Independent = 16.7% Sum 6 36 = 16.78% 1 36 = 2.78%

  5. Dice Probabilities Probability Distribution

  6. 1600’s: Probability& Gambling Blaise Pascal Do these have equal probabilities? Chevalier de Méré one "6" in four rolls  one double-six in 24 throws

  7. Prediction Model: Dice ? Y = 1 6 = 16.7% No Predictor Variables

  8. Prediction Model: Heights Linear Regression invented in 1877 by Francis Galton ChildHeight FatherHeight + MotherHeight + Gender + Ɛ = Predictor Variables!!!

  9. Prediction Model: Logistic Logistic Regression invented in 1838 by Pierre-Francois Verhulst

  10. Probability & Classification: Gender ~ Height Let’s Invert the Problem – “Given Child Height What is the Gender?” and Pretend its 1761 – Before Logistic Regression Gender (Categorical) (Continuous) ChildHeight

  11. 1761: Bayesian Child Height Gender = Probability Female Probability Distribution Height of the Person Probability Male New Data = 67.5 75 66.5 60 Prior (X) Data Prior (X) Data Prior (X) Prior (X)

  12. Bayesian Formulas 0.49 0.51 Same for both female and male

  13. Normal Distribution and Probability 2.6 69.2 65.5 61.3 D D

  14. Bayesian Formulas D D 60 5.549099 66.5 D 6.884877 67.5 75

  15. Bayesian Formulas – Excel D

  16. Naïve Bayes 84.1%

  17. Naïve Bayes

  18. Probability: Gender ~ Height + Weight + FootSize

  19. Probability: Gender ~ Height + Weight + FootSize

  20. Probability: Gender ~ Height + Weight + FootSize

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