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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 5.5  Lognormal model in Python using Stan

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import numpy as np
from scipy.stats import uniform, lognorm
import pystan

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# Data
np.random.seed(1056)                             # set seed to replicate example
nobs= 5000                                              # number of obs in model
x1 = uniform.rvs(size=nobs)                   # random uniform variable

beta0 = 2.0                                               # intercept
beta1 = 3.0                                               # linear predictor
sigma = 1.0                                              # dispersion
xb = beta0 + beta1 * x1                           # linear predictor, xb
exb = np.exp(xb)

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y = lognorm.rvs(sigma, scale=exb, size=nobs)       # create y as adjusted
# random normal variate
# Fit
mydata = {}
mydata['N'] = nobs
mydata['x1'] = x1
mydata['y'] = y

stan_lognormal = """
data{
int<lower=0> N;
vector[N] x1;
vector[N] y;
}
parameters{
real beta0;
real beta1;
real<lower=0> sigma;
}
transformed parameters{
vector[N] mu;

for (i in 1:N) mu[i] = beta0 + beta1 * x1[i];
}
model{
y ~ lognormal(mu, sigma);
}
"""

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# fit
fit = pystan.stan(model_code=stan_lognormal, data=mydata, iter=5000, chains=3,
verbose=False, n_jobs=3)

# Output
nlines = 8                                                            # number of lines in output

output = str(fit).split('\n')
for item in output[:nlines]:
print(item)

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Output on screen:

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Inference for Stan model: anon_model_74e214ef8b541b8d71bc91e76ef3dd3d.
3 chains, each with iter=5000; warmup=2500; thin=1;
post-warmup draws per chain=2500, total post-warmup draws=7500.

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mean      se_mean          sd        2.5%         25%         50%         75%       97.5%       n_eff        Rhat
beta0           1.99          5.0e-4       0.03        1.93         1.97          1.99         2.00           2.04     2798.0          1.0
beta1           3.00          8.9e-4       0.05        2.91         2.97          3.00         3.03           3.09     2685.0          1.0
sigma          0.99          1.5e-4    9.4e-3       0.97          0.98          0.99         1.00           1.01     3838.0          1.0

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