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

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

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

​

# Data
path_to_data = 'https://raw.githubusercontent.com/astrobayes/BMAD/master/data/Section_10p7/GCs.csv'

data_frame = dict(pd.read_csv(path_to_data))

​

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

​

# 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;

​

    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));
}
"""

​

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

​

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

​

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

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

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