NOTE: This is an experimental version of PyStan 3. Do not use! If you must use this, install it in a virtualenv so it will not conflict with Pystan 2.x.

Python interface to Stan, a package for Bayesian inference.

Stan® is a state-of-the-art platform for statistical modeling and high-performance statistical computation. Thousands of users rely on Stan for statistical modeling, data analysis, and prediction in the social, biological, and physical sciences, engineering, and business.

• Open source software: ISC License

This is an example in Section 5.5 of Gelman et al (2003), which studied coaching effects from eight schools. For simplicity, we call this example "eight schools."

import pystan
program_code = """
data {
  int<lower=0> J; // number of schools
  real y[J]; // estimated treatment effects
  real<lower=0> sigma[J]; // s.e. of effect estimates
}
parameters {
  real mu;
  real<lower=0> tau;
  real eta[J];
}
transformed parameters {
  real theta[J];
  for (j in 1:J)
    theta[j] = mu + tau * eta[j];
}
model {
  target += normal_lpdf(eta | 0, 1);
  target += normal_lpdf(y | theta, sigma);
}
"""

data = {'J': 8,
        'y': [28,  8, -3,  7, -1,  1, 18, 12],
        'sigma': [15, 10, 16, 11,  9, 11, 10, 18]}

posterior = pystan.compile(program_code, data=data)
fit = posterior.sample(num_chains=4, num_samples=1000)
df = fit.to_frame()  # yields a pandas `DataFrame`

Install from source in a virtualenv.