In [44]:

    

import pandas as pd
import numpy as np
from __future__ import division # this is to avoid problems when we divide integers (remember 3/5=0 in Python 2, unless we do this step)


    

In [47]:

    

# read in Ch 6 data on Meningitis diagnosis
df = pd.read_csv('./Table6-1.csv', skiprows=[0], names=['ID', 'Headache', 'Fever', 'Vomiting', 'Meningitis'])

df.head()


    

    
Out[47]:






  

    

      

      
ID
      
Headache
      
Fever
      
Vomiting
      
Meningitis
    
  
  

    

      
0
      
1
      
true
      
true
      
false
      
false
    
    

      
1
      
2
      
false
      
true
      
false
      
false
    
    

      
2
      
3
      
true
      
false
      
true
      
false
    
    

      
3
      
4
      
true
      
false
      
true
      
false
    
    

      
4
      
5
      
false
      
true
      
false
      
true
    
  

In [51]:

    

# from the data, probability of having headache, no fever, and vomiting, regardless of meningitis diagnosis
Phnfv = len(df[np.logical_and(df.Headache.str.strip()=='true', np.logical_and(df.Fever.str.strip()=='false', df.Vomiting.str.strip()=='true'))])/len(df)

# from the data, probability of having meningitis, regardless of symptoms
Pm = sum(df.Meningitis.str.strip()=='true')/len(df)

# from the data, probability of having headache, no fever, and vomiting, given a positive meningitis diagnosis
Phnfv_g_m = len(df[np.logical_and(df.Meningitis.str.strip()=='true',np.logical_and(df.Headache.str.strip()=='true', np.logical_and(df.Fever.str.strip()=='false', df.Vomiting.str.strip()=='true')))])/sum(df.Meningitis.str.strip()=='true')


    

In [52]:

    

# Bayes' Theorem: 
# P(meningitis|headache, no fever, vomiting) = P(headache, no fever, vomiting|meningitis)P(meningitis)/P(headache, no fever, vomiting)
# ... so probability that the patient with headache, no fever and vomiting has meningitis is:
Phnfv_g_m*Pm/Phnfv


    

    
Out[52]:





0.33333333333333331

In [59]:

    

# probability of headache given positive meningitis diagnosis
Ph_g_m = len(df[np.logical_and(df.Meningitis.str.strip()=='true',df.Headache.str.strip()=='true')])/sum(df.Meningitis.str.strip()=='true')

# probability of no fever given positive meningitis diagnosis
Pnf_g_m = len(df[np.logical_and(df.Meningitis.str.strip()=='true',df.Fever.str.strip()=='false')])/sum(df.Meningitis.str.strip()=='true')

# probability of vomiting given positive meningitis diagnosis
Pv_g_m = len(df[np.logical_and(df.Meningitis.str.strip()=='true',df.Vomiting.str.strip()=='true')])/sum(df.Meningitis.str.strip()=='true')

# probability of headache given negative meningitis diagnosis
Ph_g_nm = len(df[np.logical_and(df.Meningitis.str.strip()=='false',df.Headache.str.strip()=='true')])/sum(df.Meningitis.str.strip()=='false')

# probability of no fever given negative meningitis diagnosis
Pnf_g_nm = len(df[np.logical_and(df.Meningitis.str.strip()=='false',df.Fever.str.strip()=='false')])/sum(df.Meningitis.str.strip()=='false')

# probability of vomiting, given negative meningitis diagnosis
Pv_g_nm = len(df[np.logical_and(df.Meningitis.str.strip()=='false',df.Vomiting.str.strip()=='true')])/sum(df.Meningitis.str.strip()=='false')


    

In [60]:

    

# to sum it up, here are the probabilities of headache, no fever, and vomiting, given a positive meningitis diagnosis...
print Ph_g_m, Pnf_g_m, Pv_g_m


    

    




0.666666666667 0.666666666667 0.666666666667

In [41]:

    

# ... and here are the probabilities of headache, no fever, and vomiting, given a negative meningitis diagnosis
print Ph_g_nm, Pnf_g_nm, Pv_g_nm


    

    




0.714285714286 0.571428571429 0.571428571429

In [62]:

    

# overall probability of having headache, no fever, and vomiting (assuming conditional independence between all symptoms)
# (this is the denominator for naive Bayes estimator)
Ph_g_m*Pnf_g_m*Pv_g_m*Pm + Ph_g_nm*Pnf_g_nm*Pv_g_nm*(1-Pm)


    

    
Out[62]:





0.25215419501133784

In [63]:

    

# probability of headache, no fever, and vomiting (assuming conditional independence between all symptoms)
# (this is the numerator for naive Bayes estimator)
Ph_g_m*Pnf_g_m*Pv_g_m*Pm


    

    
Out[63]:





0.088888888888888878

In [64]:

    

# Naive Bayes: assuming that all symptoms are conditionally independent,
# P(meningitis|headache, no fever, vomiting) = P(headache|meningitis)P(no fever|meningitis)P(vomiting|meningitis)P(meningitis)/ 
#                                                       (P(headache|meningitis)P(no fever|meningitis)P(vomiting|meningitis)P(meningitis)+
#                                                          P(headache|no meningitis)P(no fever|no meningitis)P(vomiting|no meningitis)P(no meningitis))
# so probability of meningitis given headache, no fever, and vomiting is approx.:
Ph_g_m*Pnf_g_m*Pv_g_m*Pm/(Ph_g_m*Pnf_g_m*Pv_g_m*Pm + Ph_g_nm*Pnf_g_nm*Pv_g_nm*(1-Pm))


    

    
Out[64]:





0.35251798561151076