Question

We’ll repeat the example of determining the bias of a coin from observed coin tosses. The likelihood is binomial, and we use a beta prior.

Note the different API from PyMC2.

n = 100
h = 61
alpha = 2
beta = 2

niter = 1000
with pm.Model() as model: # context management
    # define priors
    p = pm.Beta('p', alpha=alpha, beta=beta)

    # define likelihood
    y = pm.Binomial('y', n=n, p=p, observed=h)

    # inference
    start = pm.find_MAP() # Use MAP estimate (optimization) as the initial state for MCMC
    step = pm.Metropolis() # Have a choice of samplers
    trace = pm.sample(niter, step, start, random_seed=123, progressbar=True)

[-----------------100%-----------------] 1000 of 1000 complete in 0.2 sec

plt.hist(trace['p'], 15, histtype='step', normed=True, label='post');
x = np.linspace(0, 1, 100)
plt.plot(x, stats.beta.pdf(x, alpha, beta), label='prior');
plt.legend(loc='best');