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

2. Medieval Times: Dice and Gambling

3. Modern Times: Dice and Games/Gambing

4. Dice Probabilities 1616 =16.7% 123456 1234567 2345678 3456789 45678910 56789 11 6789101112 1 36 = 2.78% 6 36 =16.78% Dice Outcome are Independent Sum

5. Dice Probabilities 123456 1234567 2345678 3456789 45678910 56789 11 6789101112 Probability Distribution

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

7. Prediction Model: Dice 1616 =16.7% Y = ? No Predictor Variables

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

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 ChildHeight (Categorical)(Continuous)

11. 1761: Bayesian Probability Distribution New Data Probability Female Probability Male Height of the Person = Data Prior (X) Data Prior (X) 60 67.575 = Gender Prior (X) Child Height 66.5

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

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

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

15. Bayesian Formulas – Excel D

16. Naïve Bayes 84.1%

17. Naïve Bayes

18. Probability: Gender ~ Height + Weight + FootSize