beta_binom_arviz.py

import superimport

from scipy.stats import beta

np.random.seed(42)
theta_real = 0.35
ntrials = 100
data = stats.bernoulli.rvs(p=theta_real, size=ntrials)

N = ntrials; N1 = sum(data); N0 = N-N1; # Sufficient statistics
aprior = 1; bprior = 1; # prior
apost = aprior + N1; bpost = bprior + N0 # posterior

# Interval function
alpha = 0.05
CI1 = beta.interval(1-alpha, apost, bpost)
print('{:0.2f}--{:0.2f}'.format(CI1[0], CI1[1])) # (0.06:0.52) 

# Use the inverse CDF (percent point function)
l  = beta.ppf(alpha/2, apost, bpost)
u  = beta.ppf(1-alpha/2, apost, bpost)
CI2 = (l,u)
print('{:0.2f}--{:0.2f}'.format(CI2[0], CI2[1])) # (0.06:0.52) 

# Use Monte Carlo sampling
samples = beta.rvs(apost, bpost, size=10000)
samples = np.sort(samples)
CI3 = np.percentile(samples, 100*np.array([alpha/2, 1-alpha/2])) 
print('{:0.2f}--{:0.2f}'.format(CI3[0], CI3[1])) # (0.06:0.51) 
print(np.mean(samples))