From: Bayesian Models for Astrophysical Data, Cambridge Univ. Press

(c) 2017,  Joseph M. Hilbe, Rafael S. de Souza and Emille E. O. Ishida 

 

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Code 10.25 Negative binomial model (AR1) in Python using Stan, for assessing the evolution of the number of sunspots through the years.

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import numpy as np
import pandas as pd
import pystan 
import statsmodels.api as sm

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# Data
path_to_data = "https://raw.githubusercontent.com/astrobayes/BMAD/master/data/Section_10p10/sunspot.csv"

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# read data
data_frame = dict(pd.read_csv(path_to_data))

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# prepare data for Stan
data = {}
data['Y'] = [int(round(item)) for item in data_frame['nspots']]
data['nobs'] = len(data['Y'])
data['K'] = 2

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# Fit
stan_code="""
data{
    int<lower=0> nobs;                # number of data points
    int<lower=0> K;                    # number of coefficients
    int Y[nobs];                            # nuber of sunspots
}
parameters{
    vector[K] phi;                         # linear predictor coefficients
    real<lower=0> theta;              # noise parameter
}
model{
    vector[nobs] mu;
    
    mu[1] = Y[1];                         # set initial value

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    for (t in 2:nobs) mu[t] = exp(phi[1] + phi[2] * Y[t - 1]);

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    # priors and likelihood
    theta ~ gamma(0.001, 0.001);
    for (i in 1:K) phi[i] ~ normal(0, 100);

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    Y ~ neg_binomial_2(mu, theta);
}
"""

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# Run mcmc
fit = pystan.stan(model_code=stan_code, data=data, iter=7500, chains=3,
                           warmup=5000, thin=1, n_jobs=3)

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# Output
print(fit)

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