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

Medieval Times: Dice and Gambling

Modern Times: Dice and Games/Gambing

Dice Probabilities 1616 =16.7% = 2.78% 6 36 =16.78% Dice Outcome are Independent Sum

Dice Probabilities Probability Distribution

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

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

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

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

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)

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

Bayesian Formulas Same for both female and male

Normal Distribution and Probability D D

Bayesian Formulas D D D

Bayesian Formulas – Excel D

Naïve Bayes 84.1%

Naïve Bayes

Probability: Gender ~ Height + Weight + FootSize