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 10.11 Beta model in Python using Stan, for accessing the relationship between the fraction of atomic gas and the galaxy stellar mass

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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 = 'https://raw.githubusercontent.com/astrobayes/BMAD/master/data/Section_10p5/f_gas.csv'

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# read data
data_frame = dict(pd.read_csv(path_to_data))

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# built atomic gas fraction
y = np.array([data_frame['M_HI'][i] / (data_frame['M_HI'][i] + data_frame['M_STAR'][i])
                      for i in range(data_frame['M_STAR'].shape[0])])

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x = np.array([np.log(item) for item in data_frame['M_STAR']])

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# prepare data for Stan
data = {}
data['Y'] = y
data['X'] = sm.add_constant((x.transpose()))
data['nobs'] = data['X'].shape[0]
data['K'] = data['X'].shape[1]

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# Fit
stan_code="""
data{
    int<lower=0> nobs;                                         # number of data points
    int<lower=0> K;                                              # number of coefficients
    matrix[nobs, K] X;                                           # stellar mass
    real<lower=0, upper=1> Y[nobs];                   # atomic gas fraction
}
parameters{
    vector[K] beta;                                                 # linear predictor coefficients
    real<lower=0> theta;
}
model{
    vector[nobs] pi;
    real a[nobs];
    real b[nobs];
    
    for (i in 1:nobs){
       pi[i] = inv_logit(X[i] * beta);
       a[i]  = theta * pi[i];
       b[i]  = theta * (1 - pi[i]);
    } 

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    # priors and likelihood
    for (i in 1:K) beta[i] ~ normal(0, 100);
    theta ~ gamma(0.01, 0.01);

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    Y ~ beta(a, b);
}
"""

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# Run mcmc
fit = pystan.stan(model_code=stan_code, data=data, iter=7500, chains=3,
                            warmup=5000, thin=1, n_jobs=3)

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# Output
print(fit)

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