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import matplotlib.pyplot as plt
%matplotlib inline
%config InlineBackend.figure_format = 'svg' 
import numpy as np
import scipy as sp

Method A: keep edge w.p. $p_s$



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np.random.uniform(size=10)>0.1









    Out[3]:





array([ True,  True,  True,  True,  True,  True,  True,  True,  True,  True], dtype=bool)



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def method_a_sim(dout, ps, nsamples=100000):
    samples = [0]*nsamples
    for i in range(nsamples):
        if np.random.uniform() < ps:
            nedges = 1 + np.random.binomial(dout-1, ps)
            samples[i] = 1/float(nedges)
    return np.mean(samples), np.std(samples)



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def method_a_analysis(dout,ps):
    return ( 1 - (1-ps)**dout )/float(dout)



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dout = 3



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samples = method_a_sim(dout, ps)



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samples









    Out[14]:





(0.33247999999999994, 0.14006682785965657)



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method_a_analysis(dout,ps)









    Out[15]:





0.333



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Method B: $1$ edge uniformly and Binomial from the rest



In [16]:

    
def method_b_sim(dout, ps, nsamples=100000):
    samples = [0]*nsamples
    for i in range(nsamples):
        if np.random.uniform() < 1/float(dout):
            nedges = 1 + np.random.binomial(dout-1, ps)
            samples[i] = 1/float(nedges)
        else:
            if np.random.uniform() < ps:
                nedges = 2 + np.random.binomial(dout-2, ps)
                samples[i] = 1/float(nedges)
    return np.mean(samples), np.std(samples)
#    return sum(samples)/float(len(samples))



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def method_b_analysis(dout,ps):
    return 1 /float(dout)



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ps=0.9



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method_b_sim(dout,ps)









    Out[19]:





(0.33333833333333335, 0.11090160793093429)



In [20]:

    
method_b_analysis(dout,ps)









    Out[20]:





0.3333333333333333



In [21]:

    
dout=8
allps = np.linspace(0.01, 1)



In [22]:

    
meanstda = [method_a_sim(dout, ps) for ps in allps]
(meana, stda) = zip(*meanstda)
meana = np.array(meana)
stda = np.array(stda)



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analytica = [method_a_analysis(dout,ps) for ps in allps]



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meanstdb = [method_b_sim(dout, ps) for ps in allps]
(meanb, stdb) = zip(*meanstdb)
meanb = np.array(meanb)
stdb = np.array(stdb)



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analyticb = [method_b_analysis(dout,ps) for ps in allps]



In [26]:

    
fig, ax = plt.subplots(1)
ax.plot(allps, analytica, lw=2, label='Method A: analysis', color='blue')
ax.plot(allps, meana, '--', lw=2, label='Method A: analysis', color='black')
ax.plot(allps, analyticb, lw=2, label='Method B: analysis', color='yellow')
ax.plot(allps, meanb, '--', lw=2, label='Method A: analysis', color='black')
ax.fill_between(allps, meana+stda, meana-stda, facecolor='blue', alpha=0.5)
ax.fill_between(allps, meanb+stdb, meanb-stdb, facecolor='yellow', alpha=0.5)

ax.axis([0, 1, 0, 2/float(dout)]);



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