In [19]:

    

import pymc as pm
%matplotlib inline


    

In [2]:

    

N = 100
p = pm.Uniform("freq_cheating", 0, 1)


    

In [3]:

    

true_answers = pm.Bernoulli("truths", p, size=N)


    

In [6]:

    

first_coin_flips = pm.Bernoulli("first_flips", 0.5, size=N)


    

In [8]:

    

second_coin_flips = pm.Bernoulli("second_flips", 0.5, size=N)


    

In [9]:

    

@pm.deterministic
def observed_proportion(t_a=true_answers,
                        fc=first_coin_flips,
                        sc=second_coin_flips):

    observed = fc * t_a + (1 - fc) * sc
    return observed.sum() / float(N)


    

In [10]:

    

observed_proportion.value


    

    
Out[10]:





0.56999999999999995

In [12]:

    

X = 35
observations = pm.Binomial("obs", N, observed_proportion, observed=True,
                           value=X)


    

In [13]:

    

model = pm.Model([p, true_answers, first_coin_flips,
                  second_coin_flips, observed_proportion, observations])

# To be explained in Chapter 3!
mcmc = pm.MCMC(model)
mcmc.sample(40000, 15000)


    

    




 [-----------------100%-----------------] 40000 of 40000 complete in 14.2 sec

In [21]:

    

pm.Matplot.plot(mcmc);


    

    




Plotting freq_cheating
Plotting observed_proportion






    













    

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