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 6.23 Zero-truncated Poisson 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, binom, poisson

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def  ztpoisson(N, lambda_par):
    """Zero truncated Poisson distribution."""

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    temp = poisson.pmf(0, lambda_par)                
    p = [uniform.rvs(loc=item, scale=1-item) for item in temp]
    ztp = [int(poisson.ppf(p[i],lambda_par[i])) for i in range(N)]
  
    return np.array(ztp)

# Data
np.random.seed(123579)                                                # set seed to replicate example
nobs= 3000                                                                     # number of obs in model 

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x1 = binom.rvs(1, 0.3, size=nobs)
x2 = binom.rvs(1, 0.6, size=nobs)
x3 = uniform.rvs(size=nobs)

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xb = 1.0 + 2.0 * x1 - 3.0 * x2 - 1.5 * x3                         # linear predictor

exb = np.exp(xb)          

ztpy = ztpoisson(nobs, exb)                                           # create y as adjusted

X = np.column_stack((x1,x2,x3))
X = sm.add_constant(X)

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# Fit
mydata = {}                                                                  # build data dictionary
mydata['N'] = nobs                                                       # sample size
mydata['X'] = X                                                            # predictors         
mydata['Y'] = ztpy                                                        # response variable
mydata['K'] = X.shape[1]                                             # number of coefficients

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stan_code = """
data{
    int N;
    int K;
    matrix[N, K] X;
    int Y[N];
}
parameters{
    vector[K] beta;
}
model{
    vector[N] mu;

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    mu = exp(X * beta);

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    # likelihood
    for (i in 1:N) Y[i] ~ poisson(mu[i]) T[0,];
}
"""

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# Run mcmc
fit = pystan.stan(model_code=stan_code, data=mydata, iter=5000, chains=3,
                           warmup=4000, n_jobs=3)

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# Output
print(fit) 
 

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