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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

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Code 5.28 Binomial model in Python using Stan

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

from scipy.stats import uniform, poisson,  binom

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# Data
np.random.seed(33559)                                       # set seed to replicate example
nobs= 2000                                                          # number of obs in model

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m = 1 + poisson.rvs(5, size=nobs)
x1 = uniform.rvs(size=nobs)                               # random uniform variable
x2 = uniform.rvs(size=nobs)

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beta0 = -2.0
beta1 = -1.5
beta2 = 3.0

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xb = beta0 + beta1 * x1 + beta2 * x2
exb = np.exp(xb)
p = exb / (1 + exb)
y = binom.rvs(m, p)                                            # create y as adjusted

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mydata = {}
mydata['K'] = 3
mydata['N'] = nobs
mydata['Y'] = y
mydata['m'] = m

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# Fit
stan_code = """
data{
int<lower=0> N;
int<lower=0> K;
matrix[N, K] X;
int Y[N];
int m[N];
}
parameters{
vector[K] beta;
}
transformed parameters{
vector[N] eta;
vector[N] p;

eta = X * beta;

for (i in 1:N) p[i] = inv_logit(eta[i]);
}
model{
Y ~ binomial(m, p);
}

"""

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fit = pystan.stan(model_code=stan_code, data=mydata, iter=5000, chains=3,
warmup=3000, n_jobs=3)

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# Output
nlines = 8

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

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Output on screen:

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Inference for Stan model: anon_model_a8d38d4e306eceb01846fe26ab1590a3.
3 chains, each with iter=5000; warmup=3000; thin=1;
post-warmup draws per chain=2000, total post-warmup draws=6000.

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mean      se_mean           sd       2.5%        25%        50%      75%      97.5%        n_eff     Rhat
beta[0]         -2.07          1.3e-3        0.06        -2.2       -2.12       -2.07      -2.03       -1.96      2229.0        1.0
beta[1]         -1.56          1.6e-3        0.08       -1.71      -1.61       -1.55        -1.5         -1.4      2355.0        1.0
beta[2]          3.15          1.8e-3        0.09        2.98        3.09        3.15        3.21        3.32      2377.0        1.0

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