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 6.25 Zero-truncated negative binomial 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, nbinom, bernoulli

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def gen_ztnegbinom(n, mu, size):
    """Zero truncated negative binomial distribution.

        input:  n, int
                   number of successes

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                   mu, float or int
                   number of trials

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                   size, float
                  probability of success

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        output: ztnb, list of int
                    draws from a zero truncated negative binomial distribution
    """

    temp = nbinom.pmf(0, mu, size)
    p = [uniform.rvs(loc=temp[i], scale=1-temp[i]) for i in range(n)]
    ztnb = [int(nbinom.ppf(p[i], mu[i], size)) for i in range(n)]

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    return np.array(ztnb)

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# Data
np.random.seed(123579)                                               # set seed to replicate example
nobs= 2000                                                                    # number of obs in model 

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x1 = bernoulli.rvs(0.7, size=nobs)
x2 = uniform.rvs(size=nobs)

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xb = 1.0 + 2.0 * x1 - 4.0 * x2                                         # linear predictor
exb = np.exp(xb)          
alpha = 5

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# create y as adjusted 
ztnby = gen_ztnegbinom(nobs, exb, 1.0/alpha)  

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

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

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# Fit

stan_code = """
data{
    int N;
    int K;
    matrix[N, K] X;
    int Y[N];
}
parameters{
    vector[K] beta;
    real<lower=1> alpha;
}
model{
    vector[N] mu;

    # covariates transformation
    mu = exp(X * beta);      
   
    # likelihood
    for (i in 1:N) Y[i] ~ neg_binomial(mu[i], 1.0/(alpha - 1.0)) T[0,];
}
"""

# Run mcmc
fit = pystan.stan(model_code=stan_code, data=mydata, iter=5000, chains=3,
                            warmup=2500, n_jobs=3)

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# Output
nlines = 9                                                                    # 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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