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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 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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ztnby = gen_ztnegbinom(nobs, exb, 1.0/alpha)

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

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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Output on screen:

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Inference for Stan model: anon_model_3c81b600330a0f365ece0ccee9726af6.
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
beta[0]         0.96          1.5e-3        0.08         0.8       0.91      0.97       1.02       1.12 2966.0    1.0
beta[1]         2.07          1.1e-3        0.07       1.94       2.02      2.07       2.11          2.2 3405.0    1.0
beta[2]        -3.96          1.1e-3       0.07      -4.09      -4.01     -3.96     -3.92       -3.83 4033.0    1.0
alpha            4.84          2.8e-3       0.18        4.51       4.72      4.83       4.96        5.21     4100.0    1.0

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