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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 10.19 Bernoulli logit model, in Python using Stan, for assessing the relationship between Seyfert AGN activity and galactocentric distance

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

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

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x1 = data_frame['logM200']
x2 = data_frame['r_r200']

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data = {}
data['Y'] = data_frame['bpt']
data['X'] = sm.add_constant(np.column_stack((x1,x2)))
data['K'] = data['X'].shape[1]
data['N'] = data['X'].shape[0]
data['gal'] = [0 if item == data_frame['zoo'][0] else
for item in data_frame['zoo']]
data['P'] = 2

# Fit
stan_code="""
data{
int<lower=0> N;                                                      # number of data points
int<lower=0> K;                                                      # number of coefficients
int<lower=0> P;                                                       # number of populations
matrix[N,K] X;                                                         # [logM200, galactocentric distance]
int<lower=0, upper=1> Y[N];                                  # Seyfert 1/AGN 0
int<lower=0, upper=1> gal[N];                                # elliptical 0/spiral 1
}
parameters{
matrix[K,P] beta;
real<lower=0> sigma;
real mu;
}
model{
vector[N] pi;

for (i in 1:N) {
if (gal[i] == gal[1]) pi[i] = dot_product(col(beta,1),X[i]);
else pi[i] = dot_product(col(beta,2), X[i]);
}

# shared hyperpriors
sigma ~ gamma(0.001, 0.001);
mu ~ normal(0, 100);

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# priors and likelihood
for (i in 1:K) {
for (j in 1:P) beta[i,j] ~ normal(mu, sigma);
}

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Y ~ bernoulli_logit(pi);
}
"""

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# Run mcmc
fit = pystan.stan(model_code=stan_code, data=data, iter=60000, chains=3,
warmup=30000, thin=10, n_jobs=3)

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# Output
print(fit)

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Output on screen:

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Inference for Stan model: anon_model_540051ae737bb985bed8ad3b87a52b84.
3 chains, each with iter=60000; warmup=30000; thin=10;
post-warmup draws per chain=3000, total post-warmup draws=9000.

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mean     se_mean        sd       2.5%        25%        50%       75%      97.5%       n_eff       Rhat
beta[0,0]       0.04         1.6e-3     0.08       -0.11       -0.02        0.03       0.09         0.22         2491         1.0
beta[1,0]     -0.15          3.8e-3       0.1      -0.35       -0.22       -0.15      -0.07         0.02          650          1.0
beta[2,0]      0.17          5.5e-3     0.12      -0.03         0.08        0.17       0.26         0.42          467          1.0
beta[0,1]   3.1e-4         8.3e-4      0.05        -0.1        -0.03    5.3e-5       0.03            0.1       3509          1.0
beta[1,1]     -0.02         7.6e-4      0.05      -0.12        -0.05     -0.02       0.01          0.07       4246          1.0
beta[2,1]   4.9e-3         7.0e-4      0.05      -0.09        -0.03   4.4e-3       0.04          0.11       5304          1.0
sigma           0.14         3.8e-3      0.09       0.02         0.08       0.13       0.18          0.37        604          1.0
mu            7.0e-3         8.1e-4      0.08      -0.14        -0.03    4.9e-3       0.05          0.17      8934          1.0
lp__           -1193            0.19      2.91     -1199        -1195    -1193     -1192        -1186        247        1.01

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Samples were drawn using NUTS at Thu May  4 14:55:41 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).

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