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

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

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

# 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;

    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);
}
"""

# 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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Output on screen:

Inference for Stan model: anon_model_955d748487258410d89e68cefe178077.
3 chains, each with iter=5000; warmup=2500; thin=1; 
post-warmup draws per chain=2500, total post-warmup draws=7500.

                mean    se_mean         sd        2.5%           25%          50%           75%        97.5%       n_eff     Rhat
beta0         0.34        4.2e-4      0.02         0.29           0.32           0.34           0.35           0.38     3132.0       1.0
beta1         1.43        7.8e-4      0.04         1.35           1.40           1.43           1.46           1.52     3160.0       1.0
theta        15.10        7.3e-3      0.45       14.20         14.80         15.10         15.40         16.00     3906.0       1.0
lp__     1709.40           0.02      1.16     1706.5     1708.80     1709.60     1710.20     1710.70     3033.0       1.0

Samples were drawn using NUTS at Thu Dec 22 17:35:40 2016.
For each parameter, n_eff is a crude measure of effective sample size,
and Rhat is the potential scale reduction factor on split chains (at 
convergence, Rhat=1).