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 10.6 Multivariate Gaussian mixed model in Python, using Stan, for accessing the relationship between luminosity, period, and color in early-type contact binaries

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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_10p3/PLC.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['x1'] = np.array(data_frame['logP'])
data['x2'] = np.array(data_frame['V_I'])
data['y'] = np.array(data_frame['M_V'])
data['nobs'] = len(data['x1'])
data['type'] = np.array([1 if item == data_frame['type'][0] else 0 
                                      for item in data_frame['type']])
data['M'] = 3
data['K'] = data['M'] - 1

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# Fit
stan_code="""
data{
    int<lower=0> nobs;                # number of data points
    int<lower=1> M;                    # number of linear predicor coefficients
    int<lower=1> K;                     # number of  distinct populations
    vector[nobs] x1;                      # obs log period
    vector[nobs] x2;                      # obs color V-I
    vector[nobs] y;                        # obs luminosity
    int type[nobs];                         # system type (near/genuine contact)
}
parameters{
    matrix[M,K] beta;                    # linear predictor coefficients
    real<lower=0> sigma[K];        # scatter around linear predictor
    real mu0;
    real sigma0;
}
model{
    vector[nobs] mu;                        # linear predictor

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    for (i in 1:nobs) {
        if (type[i] == type[1])
            mu[i] = beta[1,2] + beta[2,2] * x1[i] + beta[3,2] * x2[i];
        else mu[i] = beta[1,1] + beta[2,1] * x1[i] + beta[3,1] * x2[i];
    }

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    # priors and likelihood
    mu0 ~ normal(0, 100);
    sigma0 ~ gamma(0.001, 0.001);

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    for (i in 1:K) {
        sigma[i] ~ gamma(0.001, 0.001);
        for (j in 1:M) beta[j,i] ~ normal(mu0,sigma0);
    }

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    for (i in 1:nobs){
        if (type[i] == type[1]) y[i] ~ normal(mu[i], sigma[2]);
        else y[i] ~ normal(mu[i], sigma[1]);
    }
}
"""

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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)

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# Output
nlines = 13                                          # 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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