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 8.15 Bayesian random intercept Poisson model in Python using Stan

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

from scipy.stats import norm, uniform, poisson

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# Data
np.random.seed(1656)                                                              # set seed to replicate example
N = 2000                                                                                   # number of obs in model 
NGroups = 10

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x1 = uniform.rvs(size=N)
x2 = uniform.rvs(size=N)

Groups = np.array([200 * [i] for i in range(NGroups)]).flatten()
 

a = norm.rvs(loc=0, scale=0.5, size=NGroups)
eta = 1 + 0.2 * x1 - 0.75 * x2 + a[list(Groups)]
mu = np.exp(eta)

y = poisson.rvs(mu)

X = sm.add_constant(np.column_stack((x1,x2)))
K = X.shape[1]
Nre = NGroups

model_data = {}
model_data['Y'] = y
model_data['X'] = X                              
model_data['K'] = K
model_data['N'] = N
model_data['NGroups'] = NGroups
model_data['re'] = Groups
model_data['b0'] = np.repeat(0, K) 
model_data['B0'] = np.diag(np.repeat(100, K))
model_data['a0'] = np.repeat(0, Nre)
model_data['A0'] = np.diag(np.repeat(1, Nre))

# Fit
stan_code = """
data{
    int<lower=0> N;
    int<lower=0> K;
    int<lower=0> NGroups;
    matrix[N, K] X;
    int Y[N];
    int re[N];
    vector[K] b0;
    matrix[K, K] B0;
    vector[NGroups] a0;
    matrix[NGroups, NGroups] A0;
}
parameters{
    vector[K] beta;
    vector[NGroups] a;
    real<lower=0, upper=10> sigma_re;
}
transformed parameters{
    vector[N] eta;
    vector[N] mu; 
 
    eta = X * beta;
    for (i in 1:N){ 
        mu[i] = exp(eta[i] + a[re[i]+1]);
    }
}
model{    
    sigma_re ~ cauchy(0, 25);

    beta ~ multi_normal(b0, B0);
    a ~ multi_normal(a0, sigma_re * A0);

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    Y ~ poisson(mu);  
}
"""

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fit = pystan.stan(model_code=stan_code, data=model_data, iter=5000, chains=3, thin=10,
                            warmup=4000, n_jobs=3)

 

# Output
nlines = 19                                                                  # number of lines in screen output

 

output = str(fit).split('\n')

 

for item in output[:nlines]:
    print(item)  

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