Think Bayes

In [12]:

    

# Configure Jupyter so figures appear in the notebook
%matplotlib inline

# Configure Jupyter to display the assigned value after an assignment
%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'

# import classes from thinkbayes2
from thinkbayes2 import Pmf, Beta, MakeBinomialPmf

import thinkplot

import numpy as np


    

In [25]:

    

beta = Beta(5, 5)
prior = beta.MakePmf()
thinkplot.Pdf(prior)
thinkplot.decorate(xlabel='Prob Red Sox win (x)',
                   ylabel='PDF')


    

In [26]:

    

%psource beta.Update


    

In [27]:

    

beta.Update((15, 0))
posterior = beta.MakePmf()

thinkplot.Pdf(prior, color='gray', label='prior')
thinkplot.Pdf(posterior, label='posterior')
thinkplot.decorate(xlabel='Prob Red Sox win (x)',
                   ylabel='PDF')


    

In [28]:

    

posterior.Mean()


    

    
Out[28]:





0.8000000040157967

In [29]:

    

posterior.MAP()


    

    
Out[29]:





0.83

In [30]:

    

posterior.CredibleInterval()


    

    
Out[30]:





(0.66, 0.91)

In [31]:

    

x = posterior.Random()


    

    
Out[31]:





0.94

In [32]:

    

np.sum(np.random.random(7) < x)


    

    
Out[32]:





7

In [33]:

    

def simulate(k, dist):
    x = dist.Random()
    return np.sum(np.random.random(k) <= x)
    
simulate(7, posterior)


    

    
Out[33]:





6

In [34]:

    

sample = [simulate(7, posterior) for i in range(100000)];
thinkplot.Hist(Pmf(sample))


    

In [35]:

    

np.mean(np.array(sample) >= 4)


    

    
Out[35]:





0.94716

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