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 7.12 Bayesian log-gamma–logit hurdle model in Python using Stan

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import numpy as np
import pystan
import statsmodels.api as sm
from scipy.stats import uniform, gamma, bernoulli

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# Data
np.random.seed(33559)                                                  # set seed to replicate example
nobs = 1000                                                                    # number of obs in model

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# Generate predictors, design matrix
x1 = uniform.rvs(loc=0, scale=4, size=nobs)
xc = -1 + 0.75 * x1
exc = np.exp(xc)
phi = 0.066
r = 1.0/phi
y = np.random.gamma(shape=exc, scale=r)

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# Construct filter
xb = -2 + 1.5 * x1
pi = 1 / (1 + np.exp(-xb))
bern = bernoulli.rvs(1 - pi)
gy = [y[i]  * bern[i] for i in range(nobs)]              # add structural zeros

X = np.transpose(x1)
X = sm.add_constant(X)

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# Fit
mydata = {}                                                          # build data dictionary
mydata['Y'] = gy                                                   # response variable
mydata['N'] = nobs                                               # sample size
mydata['Xb'] = X                                                  # predictors
mydata['Xc'] = X
mydata['Kb'] = X.shape[1]                                   # number of coefficients
mydata['Kc'] = X.shape[1]

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stan_code = """
data{
    int N;
    int Kb;
    int Kc;
    matrix[N, Kb] Xb;
    matrix[N, Kc] Xc;
    real<lower=0> Y[N];
}
parameters{
    vector[Kc] beta;
    vector[Kb] gamma;
    real<lower=0> phi;
}
model{
    vector[N] mu;
    vector[N] Pi;

    mu = exp(Xc  *  beta);

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    for (i in 1:N) Pi[i] = inv_logit(Xb[i] * gamma);

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    for (i in 1:N) {
        (Y[i] == 0) ~ bernoulli(Pi[i]);
        if (Y[i] > 0) Y[i] ~ gamma(mu[i], phi) T[0,];
    }
}
"""

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# Run mcmc
fit = pystan.stan(model_code=stan_code, data=mydata, iter=6000, chains=3,
                            warmup=4000, n_jobs=3)

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# Output
print(fit)

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