Question

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

# generate observed data
N = 100
_mu = np.array([10])
_sigma = np.array([2])
y = np.random.normal(_mu, _sigma, N)

niter = 1000
with pm.Model() as model:
    # define priors
    mu = pm.Uniform('mu', lower=0, upper=100, shape=_mu.shape)
    sigma = pm.Uniform('sigma', lower=0, upper=10, shape=_sigma.shape)

    # define likelihood
    y_obs = pm.Normal('Y_obs', mu=mu, sd=sigma, observed=y)

    # inference
    start = pm.find_MAP()
    step = pm.Slice()
    trace = pm.sample(niter, step, start, random_seed=123, progressbar=True)

[-----------------100%-----------------] 1000 of 1000 complete in 1.9 sec

plt.figure(figsize=(10,4))
plt.subplot(1,2,1);
plt.hist(trace['mu'][-niter/2:,0], 25, histtype='step');
plt.subplot(1,2,2);
plt.hist(trace['sigma'][-niter/2:,0], 25, histtype='step');