ipython for https://stats.stackexchange.com/questions/114139/inferring-prior-distribution/114219#114219

inf.py

paste 
from pymc.Matplot import plot as mcplot
mcplot(mcmc)
%pylab
paste
mcmc.trace('alpha')
mcmc.trace('alpha')[:]
hist(mcmc.trace('alpha')[:])
hist(mcmc.trace('alpha')[:], normed=True, bins=25)
hist(mcmc.trace('alpha')[:], normed=True, bins=25)
plt.title("posterior of alpha")
hist(mcmc.trace('alpha')[:], normed=True, bins=25, label='posterior of alpha', alpha=0.7)
hist(mcmc.trace('beta')[:], normed=True, bins=25, label='posterior of beta', alpha=0.7)
hist(mcmc.trace('beta')[:], normed=True, bins=25, label='posterior of beta', alpha=0.7, histstyle='stepfilled')
hist(mcmc.trace('beta')[:], normed=True, bins=25, label='posterior of beta', alpha=0.7, histtype='stepfilled')
hist(mcmc.trace('beta')[:], normed=True, bins=25, label='posterior of beta', alpha=0.7, histtype='stepfilled')
hist(mcmc.trace('alpha')[:], normed=True, bins=25, label='posterior of alpha', alpha=0.7, histtype='stepfilled')
plt.legend()
plt.title('Posterior distribution of alpha,beta for a Beta distribution')
from scipy.stats import beta
x = linspace(0,1, 500)
alpha_trace = mcmc.trace('alpha')[:]
beta_trace = mcmc.trace('beta')[:]
alpha_trace = mcmc.trace('alpha')[:1000]
alpha_trace
alpha_trace = mcmc.trace('alpha')[::1000]
alpha_trace
beta_trace = mcmc.trace('beta')[::1000]
beta.pdf(x, alpha_trace, beta_trace)
beta.pdf(x, 1, 1)
beta.pdf(x, alpha_trace[:,None], beta_trace[:,None])
beta.pdf(x, alpha_trace[:,None], beta_trace[:,None]).shape
plot(beta.pdf(x, alpha_trace[:,None], beta_trace[:,None]))
plot(beta.pdf(x, alpha_trace[:,None], beta_trace[:,None]).T)
plot(beta.pdf(x, alpha_trace[:,None], beta_trace[:,None]).T)
plot(beta.pdf(x, alpha_trace[:,None], beta_trace[:,None]).T)
plt.title('Samples from the posterior distribution of the unknown distribution')
alpha_trace = mcmc.trace('alpha')
beta_trace = mcmc.trace('beta')
beta.pdf(x, alpha_trace[:,None], beta_trace[:,None]).shape
beta.pdf(x, alpha_trace[:,None], beta_trace[:,None]).mean(0)
beta.pdf(x, alpha_trace[:,None], beta_trace[:,None]).mean(0).shape
plot(beta.pdf(x, alpha_trace[:,None], beta_trace[:,None]).mean(0))
plot(beta.pdf(x, alpha_trace[:,None], beta_trace[:,None]).mean(0))