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 5.14 Beta model in Python using Stan

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

from scipy.stats import uniform
from scipy.stats import beta as beta_dist

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# Data
np.random.seed(1056)                                          # set seed to replicate example
nobs= 2000                                                           # number of obs in model 
x1 = uniform.rvs(size=nobs)                                # random uniform variable

beta0 = 0.3
beta1 = 1.5
theta = 15

xb = beta0 + beta1 * x1
exb = np.exp(-xb)
p = exb / (1 + exb)

y = beta_dist.rvs(theta * (1 - p), theta * p)           # create y as adjusted

 

# Fit
mydata = {}                                
mydata['N'] = nobs                                               # sample size
mydata['x1'] = x1                                                 # predictors         
mydata['y'] = y                                                     # response variable
  
stan_code = """
data{
    int<lower=0> N;
    vector[N] x1;
    vector<lower=0, upper=1>[N] y;
}
parameters{
    real beta0;
    real beta1;
    real<lower=0> theta;
}
model{
    vector[N] eta;
    vector[N] p;
    vector[N] shape1;
    vector[N] shape2;

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    for (i in 1:N){
        eta[i] = beta0 + beta1 * x1[i];
        p[i] = inv_logit(eta[i]);
        shape1[i] = theta * p[i];
        shape2[i] = theta * (1 - p[i]);
    }

    y ~ beta(shape1, shape2);
}
"""

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

 

# Output
print(fit)  
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