From: Bayesian Models for Astrophysical Data, Cambridge Univ. Press

(c) 2017,  Joseph M. Hilbe, Rafael S. de Souza and Emille E. O. Ishida  

 

you are kindly asked to include the complete citation if you used this material in a publication

Code 5.36 Beta–binomial model with synthetic data in Python using Stan

=========================================================

import numpy as np
import statsmodels.api as sm
import pystan

from scipy.stats import uniform, poisson, binom
from scipy.stats import beta as beta_dist


# Data
np.random.seed(33559)                                           # set seed to replicate example
nobs= 4000                                                              # number of obs in model 
m = 1 + poisson.rvs(5, size=nobs)
x1 = uniform.rvs(size=nobs)                                   # random uniform variable
  

beta0 = -2.0
beta1 = -1.5

eta = beta0 + beta1 * x1
sigma = 20

p = np.exp(eta) / (1 + np.exp(eta))


shape1 = sigma * p
shape2 = sigma * (1-p)

 # binomial distribution with p ~ beta
y = binom.rvs(m, beta_dist.rvs(shape1, shape2))    

     

mydata = {}
mydata['K'] = 2
mydata['X'] = sm.add_constant(np.transpose(x1))
mydata['N'] = nobs
mydata['Y'] = y
mydata['m'] = m

# Fit
stan_code = """
data{
    int<lower=0> N;
    int<lower=0> K;
    matrix[N, K] X;
    int<lower=0> Y[N];
    int<lower=1> m[N];
}
parameters{
    vector[K] beta;
    real<lower=0> sigma;
}
transformed parameters{
    vector[N] eta;
    vector[N] pi;
    vector[N] shape1;
    vector[N] shape2;
 
    eta = X * beta;


    for (i in 1:N){ 
        pi[i] = inv_logit(eta[i]); 
        shape1[i] = sigma * pi[i];
        shape2[i] = sigma * (1 - pi[i]);
    }
}
model{    

    Y ~ beta_binomial(m, shape1, shape2);  
}
"""

fit = pystan.stan(model_code=stan_code, data=mydata, iter=7000, chains=3,
                           warmup=3500, n_jobs=3)

# Output
nlines = 8

output = str(fit).split('\n')
for item in output[:nlines]:
    print(item)

=========================================================

Output on screen:

Inference for Stan model: anon_model_acf4982abace71245836d5069e425eeb.
3 chains, each with iter=7000; warmup=3500; thin=1; 
post-warmup draws per chain=3500, total post-warmup draws=10500.

                     mean      se_mean           sd        2.5%        25%         50%         75%       97.5%        n_eff       Rhat
beta[0]          -2.07          7.4e-4        0.05       -2.17         -2.1        -2.07        -2.04         -1.97      4524.0         1.0
beta[1]          -1.43          1.5e-3          0.1       -1.64         -1.5        -1.43        -1.36         -1.23      4512.0         1.0
sigma             17.9             0.03        2.19      14.16       16.36       17.72        19.25        22.83      4775.0         1.0