Question

\[X \sim \mathcal{N}(\mu, \sigma^2)\]

# generate observed data
N = 100
y = np.random.normal(10, 2, N)

# define priors
mu = pymc.Uniform('mu', lower=0, upper=100)
tau = pymc.Uniform('tau', lower=0, upper=1)

# define likelihood
y_obs = pymc.Normal('Y_obs', mu=mu, tau=tau, value=y, observed=True)

# inference
m = pymc.Model([mu, tau, y])
mc = pymc.MCMC(m)
mc.sample(iter=11000, burn=10000)

[-----------------100%-----------------] 11000 of 11000 complete in 3.2 sec

plt.figure(figsize=(10,4))
plt.subplot(121)
plt.hist(mu.trace(), 15, histtype='step', normed=True, label='post');
plt.legend(loc='best');
plt.subplot(122)
plt.hist(np.sqrt(1.0/tau.trace()), 15, histtype='step', normed=True, label='post');
plt.legend(loc='best');