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• 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 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
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 ~ Height
Let’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
67.5
75
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
