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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 10.17 Negative binomial model in Python using Stan, for modeling the relationship between globular cluster population and host galaxy visual magnitude

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

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# Data
path_to_data =

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# prepare data for Stan
data = {}
data['Y'] = np.array(data_frame['N_GC'])
data['N'] = len(data['X'])
data['K'] = 2

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# Fit
stan_code="""
data{
int<lower=0> N;                                                  # number of data points
int<lower=1> K;                                                  # number of linear predictor coefficients
matrix[N,K] X;                                                    # galaxy visual magnitude
int Y[N];                                                              # size of globular cluster population
}
parameters{
vector[K] beta;                                                      # linear predictor coefficients
real<lower=0> theta;
}
model{
vector[N] mu;                                                        # linear predictor

mu = exp(X * beta);

theta ~ gamma(0.001, 0.001);

# likelihood
Y ~ neg_binomial_2(mu, theta);
}
generated quantities{
real dispersion;
vector[N] expY;                                                        # mean
vector[N] varY;                                                        # variance
vector[N] PRes;
vector[N] mu2;

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mu2 = exp(X * beta);
expY = mu2;

for (i in 1:N){
varY[i] = mu2[i] + pow(mu2[i], 2) / theta;
PRes[i] = pow((Y[i] - expY[i]) / sqrt(varY[i]),2);
}

dispersion = sum(PRes) / (N - (K + 1));
}
"""

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# Run mcmc
fit = pystan.stan(model_code=stan_code, data=data, iter=10000, chains=3,
warmup=5000, thin=1, n_jobs=3)

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# Output
nlines = 9                                                                   # number of lines in screen output

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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_723b570e1a19f3dc30e5da8afbc7bc52.
3 chains, each with iter=10000; warmup=5000; thin=1;
post-warmup draws per chain=5000, total post-warmup draws=15000.

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mean     se_mean          sd       2.5%        25%        50%         75%        97.5%       n_eff       Rhat
beta[0]       -11.73        5.4e-3       0.33    -12.36      -11.95     -11.73       -11.51       -11.08        3645         1.0
beta[1]        -0.88        2.7e-4        0.02      -0.91        -0.89      -0.88         -0.87         -0.85        3661         1.0
theta               1.1        9.6e-4        0.07       0.97         1.05          1.1          1.15           1.25        5573        1.0
dispersion    1.93        2.2e-3          0.2       1.55         1.78        1.92           2.06          2.36        8955         1.0

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