%run github_events.py


print "Some User ids from the latest events (push, star, fork etc.) on Github."
print ids[:10]
print
print "Number of unique ids found: ", ids.shape[0]
print "Largest user id: ", ids.max()

figsize(12.5,3)
plt.hist( ids, bins = 45, alpha = 0.9)
plt.title("Histogram of %d Github User ids"%ids.shape[0] );
plt.xlabel("User id")
plt.ylabel("Frequency");

FACTOR = 1000000.

import pymc as pm

upper_bound = pm.Uniform( "n_sign_ups", ids.max()/FACTOR, (ids.max())/FACTOR + 1)
obs = pm.Uniform("obs", 0, upper_bound, value = ids/FACTOR, observed = True )

#code to be examplained in Chp. 3.
mcmc = pm.MCMC([upper_bound, obs] )
mcmc.sample( 100000, 45000)

from scipy.stats.mstats import mquantiles

samples =  mcmc.trace("n_sign_ups")[:]

hist(samples, bins = 100, 
             label = "Uniform prior",
             normed=True, alpha = 0.8, 
             histtype="stepfilled", color = "#7A68A6"  );

quantiles_mean = np.append( mquantiles( samples, [0.05, 0.5, 0.95]), samples.mean() )
print "Quantiles: ", quantiles_mean[:3]
print "Mean: ", quantiles_mean[-1]
plt.vlines( quantiles_mean, 0, 33, 
            linewidth=2, linestyles = ["--", "--", "--", "-"],
            )
plt.title("Posterior distribution of total number of Github users" )
plt.xlabel("number of users (in millions)")
plt.legend()
plt.xlim( ids.max()/FACTOR - 0.01, ids.max()/FACTOR + 0.12 );