In [1]:

    

%matplotlib notebook
from __future__ import division
from scipy.stats import binom as binomial
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
#from ipywidgets import StaticInteract, RangeWidget
import pandas as pd
from IPython.display import display
from sympy import init_printing, symbols, Eq
init_printing()


    

In [2]:

    

coin_toss = []
coin_toss.append('H T T T H H T H T H'.split())
coin_toss.append('H H H H T H H H H H'.split())
coin_toss.append('H T H H H H H T H H'.split())
coin_toss.append('H T H T T T H H T T'.split())
coin_toss.append('T H H H T H H H T H'.split())


    

In [3]:

    

df = pd.DataFrame(coin_toss)


    

In [4]:

    

df


    

    
Out[4]:






  

    

      

      
0
      
1
      
2
      
3
      
4
      
5
      
6
      
7
      
8
      
9
    
  
  

    

      
0
      
H
      
T
      
T
      
T
      
H
      
H
      
T
      
H
      
T
      
H
    
    

      
1
      
H
      
H
      
H
      
H
      
T
      
H
      
H
      
H
      
H
      
H
    
    

      
2
      
H
      
T
      
H
      
H
      
H
      
H
      
H
      
T
      
H
      
H
    
    

      
3
      
H
      
T
      
H
      
T
      
T
      
T
      
H
      
H
      
T
      
T
    
    

      
4
      
T
      
H
      
H
      
H
      
T
      
H
      
H
      
H
      
T
      
H
    
  

In [5]:

    

thetaA, thetaB = symbols('theta_A theta_B')
a,b = thetaA, thetaB # Hack to display
thetaA = 0.6
thetaB = 0.5
a , thetaA


    

    
Out[5]:





$$\left ( \theta_{A}, \quad 0.6\right )$$

In [6]:

    

b, thetaB


    

    
Out[6]:





$$\left ( \theta_{B}, \quad 0.5\right )$$

In [7]:

    

## Observed Case

observed = ['B', 'A', 'A', 'B', 'A']
index_A = [i for i,x in enumerate(observed) if x=='A']
index_B = [i for i,x in enumerate(observed) if x=='B']
total_tosses = df.size
A_tosses = df.iloc[index_A].unstack()
B_tosses = df.iloc[index_B].unstack()

A_heads = A_tosses.value_counts()['H']
B_heads = B_tosses.value_counts()['H']

theta_A = A_heads/A_tosses.size
theta_B = B_heads/B_tosses.size


    

In [8]:

    

(a, theta_A)


    

    
Out[8]:





$$\left ( \theta_{A}, \quad 0.8\right )$$

In [9]:

    

(b, theta_B)


    

    
Out[9]:





$$\left ( \theta_{B}, \quad 0.45\right )$$

In [10]:

    

thetaA = 0.6
thetaB = 0.5

def em(theta_old):
    row_prob = []
    ## Expectation
    for row in coin_toss:
        count_heads = row.count('H')
        p_a = binomial.pmf(count_heads, len(row), theta_old['A'])
        p_b = binomial.pmf(count_heads, len(row), theta_old['B'])
        p_t = p_a+p_b
        p_a = p_a/p_t
        p_b = p_b/p_t
        row_prob.append({'A': p_a, 'B': p_b, 'count_heads': count_heads})
        
    ## Maximisation
    new_coin_toss = []
    for row in row_prob:
        A_heads = 
        new_coin_tosse.append


    

    




  File "<ipython-input-10-e7842384d97a>", line 19
    A_heads =
              ^
SyntaxError: invalid syntax