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 7.8 Bayesian Poisson–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, bernoulli, poisson

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def ztp(N, lambda_):

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    temp = [poisson.pmf(0, item) for item in lambda_]
    p = [uniform.rvs(loc=item, scale=1-item) for item in temp]
    ztp = [int(poisson.ppf(p[i], lambda_[i])) for i in range(len(p))]

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    return np.array(ztp)

# Data
np.random.seed(141)                                                            # set seed to replicate example
nobs= 750                                                                             # number of obs in model 

x1 = uniform.rvs(size=nobs)

xb = 1.0 + 4.0 * x1                                                               # linear predictor
exb = np.exp(xb)       
poy = ztp(nobs, exb)

xc = -1.0 + 3.5 * x1                                                              # construct filter
pi = 1.0/(1.0 + np.exp(xc))
bern = [bernoulli.rvs(1-pi[i]) for i in range(nobs)]

poy = [poy[i]*bern[i] for i in  range(nobs)]                        # Add structural zeros

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

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# prepare data for Stan
mydata = {}                                                                        # build data dictionary
mydata['Y'] = poy                                                               # 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<lower=0> N;
    int<lower=0> Kb;
    int<lower=0> Kc;
    matrix[N, Kb] Xb;
    matrix[N, Kc] Xc;
    int<lower=0> Y[N];
}
parameters{
    vector[Kc] beta;
    vector[Kb] gamma;
    real<lower=0, upper=5.0> r;
    
}
transformed parameters{
    vector[N] mu;
    vector[N] Pi;

    mu = exp(Xc * beta);
    for (i in 1:N) Pi[i] = inv_logit(Xb[i] * gamma);
}
model{
    for (i in 1:N) {
        (Y[i] == 0) ~ bernoulli(1-Pi[i]);
        if (Y[i] > 0) Y[i] ~ poisson(mu[i]) T[1,];
    }
}
"""

# Run mcmc
fit = pystan.stan(model_code=stan_code, data=mydata, iter=7000, chains=3,
                  warmup=4000, n_jobs=3)

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# Output
nlines = 10                                                                       # 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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