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)

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

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

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

# 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);

X ~ lognormal(mu, sigma);
}
"""

# 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)

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

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

Output on screen:

3 chains, each with iter=5000; warmup=2500; thin=1;
post-warmup draws per chain=2500, total post-warmup draws=7500.

mean     se_mean        sd       2.5%        25%        50%         75%       97.5%      n_eff      Rhat
mu          -1.25         1.0e-3     0.07      -1.39        -1.3        -1.25         -1.21         -1.12      4804        1.0
sigma      1.04          7.6e-4     0.05       0.94          1.0         1.03          1.07          1.14       4612        1.0
lp__     -110.3             0.02     1.01    -113.1     -110.7      -110.0       -109.6      -109.3       3776        1.0

Samples were drawn using NUTS at Wed May  3 18:03:22 2017.
For each parameter, n_eff is a crude measure of effective sample size,
and Rhat is the potential scale reduction factor on split chains (at
convergence, Rhat=1).