# Bayesian updating — FIB 34 carbonation model
import numpy as np
from scipy import stats

# Prior: chloride threshold (Beta distribution)
alpha_prior, beta_prior = 2.5, 4.0
prior = stats.beta(alpha_prior, beta_prior)

# Likelihood from field inspection data
observed_data = [0.42, 0.38, 0.51, 0.45, 0.39]

# Posterior update
alpha_post = alpha_prior + sum(observed_data)
beta_post  = beta_prior  +\u258E