• 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

16

= 16.7%

1 2 3 4 5 6

1 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12

136 = 2.78%

636

= 16.78%

Dice Outcome are Independent

Sum

Dice Probabilities

1 2 3 4 5 61 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12

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

16

= 16.7%

Y = ?

No Predictor Variables

Prediction Model: Heights

ChildHeight = FatherHeight + MotherHeight + Gender + ƐPredictor Variables!!!

Linear Regression invented in 1877 by Francis Galton

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

Probability & Classification: Gender ~ HeightLet’s Invert the Problem – “Given Child Height What is the Gender?”

and Pretend its 1761 – Before Logistic Regression

49% 51%

female male

Gender ChildHeight(Categorical) (Continuous)

1761: Bayesian

Probability Distribution

New Data

ProbabilityFemale

ProbabilityMale

Height of the Person

=

DataPrior (X) Prior (X)

DataPrior (X)

60 67.5 75

=

Gender

Prior (X)

Child Height

66.5

Bayesian Formulas

0.49

0.51

Same for both female and male

Normal Distribution and Probability

D

D

69.2

65.5

61.3

2.6

Bayesian Formulas

60

67.575

66.56.8848775.549099

D

D

D

Bayesian Formulas – ExcelD

Naïve Bayes

84.1%

Naïve Bayes

Probability: Gender ~ Height + Weight + FootSize

Probability: Gender ~ Height + Weight + FootSize

Probability: Gender ~ Height + Weight + FootSize