Cookie Problem¶

Imports¶

import numpy as np
import scipy as sp
import matplotlib.pyplot as plt
import seaborn as sns
import empiricaldist
from empiricaldist import Pmf, Distribution

      
    

Basics Pmf¶

d6 = Pmf(); d6

	probs

for i in range(6):
#     print(i+1)
    d6[i+1] = 1
    
d6

	probs
1	1
2	1
3	1
4	1
5	1
6	1

# Pmf??

# Distribution??

d6.normalize(); d6

	probs
1	0.166667
2	0.166667
3	0.166667
4	0.166667
5	0.166667
6	0.166667

# d6

d6.mean()

3.5

d6.choice(size=10)

array([5, 5, 5, 1, 6, 2, 6, 1, 6, 2])

def decorate_dice(title):
    """Labels the axes
    title: string
    """
    
    plt.xlabel('Outcome')
    plt.ylabel('PMF')
    plt.title(title)

      
    

# d6.bar(xlabel='Outcome')
d6.bar()
decorate_dice('One die')

../_images/CookieProblem_13_0.png

twice = d6.add_dist(d6)
twice

	probs
2	0.027778
3	0.055556
4	0.083333
5	0.111111
6	0.138889
7	0.166667
8	0.138889
9	0.111111
10	0.083333
11	0.055556
12	0.027778

twice.bar()
decorate_dice('Two Dice')

../_images/CookieProblem_15_0.png

d6.add_dist??

d6.ps, d6.qs

(array([0.16666667, 0.16666667, 0.16666667, 0.16666667, 0.16666667,
        0.16666667]),
 array([1, 2, 3, 4, 5, 6]))

d6

	probs
1	0.166667
2	0.166667
3	0.166667
4	0.166667
5	0.166667
6	0.166667

twice.mean()

7.000000000000002

twice[twice.qs >3].mean()

0.10185185185185187

twice[twice.qs >3].plot.bar()

<AxesSubplot:>

../_images/CookieProblem_21_1.png

twice[twice.qs >3].mean()

0.10185185185185187

twice[1] = 0 
twice[2] = 0
twice.normalize()
twice.mean()

7.142857142857141

twice.bar()
decorate_dice('Two dice, greater than 3')

../_images/CookieProblem_24_0.png

Pmf => Prior probability
Likelihood => Multiply each prior probability by the likelihood of data
Normalize => Add all up and divide by total

Cookie Problem¶

cookie = Pmf.from_seq(['B1', 'B2']); priors

	probs
B1	0.5
B2	0.5

cookie['B1']*=0.75
cookie['B2']*=0.5
cookie

	probs
B1	0.375
B2	0.250

cookie.normalize()

0.625

cookie

	probs
B1	0.6
B2	0.4

cookie['B1']*=0.25
cookie['B2']*=0.5

cookie.normalize()

0.35

cookie

	probs
B1	0.428571
B2	0.571429

cookie2 = Pmf.from_seq(["B1", "B2"])
cookie2['B1']*= (0.75*0.25)
cookie2['B2']*=(0.5*0.5)
cookie2.normalize()

0.21875

cookie2

	probs
B1	0.428571
B2	0.571429

# cookie['B1B1']*=0.75
# cookie['B1B2']*=0.

d6.normalize??

Hypothesis Testing Dice & German Tank Problem