From: Bayesian Models for Astrophysical Data, Cambridge Univ. Press

(c) 2017,  Joseph M. Hilbe, Rafael S. de Souza and Emille E. O. Ishida 

 

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Code 10.9 Lognormal model in Python using Stan to describe the initial mass function (IMF)

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

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# Data
path_to_data = 'https://raw.githubusercontent.com/astrobayes/BMAD/master/data/Section_10p4/NGC6611.csv'

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

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# prepare data for Stan
data = {}
data['X'] = data_frame['Mass']
data['nobs'] = data['X'].shape[0]

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# Fit
stan_code="""
data{
    int<lower=0> nobs;                        # number of data points
    vector[nobs] X;                              # stellar mass
}
parameters{
    real mu;                                          # mean 
    real<lower=0> sigma;                   # scatter
}
model{
    # priors and likelihood
    sigma ~ normal(0, 100);
    mu ~ normal(0, 100);

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    X ~ lognormal(mu, sigma);
}
"""

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# Run mcmc
fit = pystan.stan(model_code=stan_code, data=data, iter=5000, chains=3,
                           warmup=2500, thin=1, n_jobs=3)

 

# Output
print(fit)

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# plot chains and posteriors
fit.traceplot()
plt.show()

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