Question

The Bayesian approach directly estimates the posterior distribution, from which all other point/interval statistics can be estimated.

a, b = 10, 10
prior = st.beta(a, b)
post = st.beta(h+a, n-h+b)
ci = post.interval(0.95)
map_ =(h+a-1.0)/(n+a+b-2.0)

xs = np.linspace(0, 1, 100)
plt.plot(prior.pdf(xs), label='Prior')
plt.plot(post.pdf(xs), label='Posterior')
plt.axvline(mu, c='red', linestyle='dashed', alpha=0.4)
plt.xlim([0, 100])
plt.axhline(0.3, ci[0], ci[1], c='black', linewidth=2, label='95% CI');
plt.axvline(n*map_, c='blue', linestyle='dashed', alpha=0.4)
plt.legend();