PyStan is a 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.

Notable features of PyStan include:

• Automatic caching of compiled Stan models
• Automatic caching of samples from Stan models
• An interface similar to that of RStan
• Open source software: ISC License

Install PyStan with pip install pystan. PyStan runs on Linux and macOS. You will also need a C++ compiler such as gcc ≥9.0 or clang ≥10.0.

The following block of code shows how to use PyStan with a model which studied coaching effects across eight schools (see Section 5.5 of Gelman et al (2003)). This hierarchical model is often called the "eight schools" model.

import stan
schools_code = """
data {
  int<lower=0> J;         // number of schools
  array[J] real y;              // estimated treatment effects
  array[J] real<lower=0> sigma; // standard error of effect estimates
}
parameters {
  real mu;                // population treatment effect
  real<lower=0> tau;      // standard deviation in treatment effects
  vector[J] eta;          // unscaled deviation from mu by school
}
transformed parameters {
  vector[J] theta = mu + tau * eta;        // school treatment effects
}
model {
  target += normal_lpdf(eta | 0, 1);       // prior log-density
  target += normal_lpdf(y | theta, sigma); // log-likelihood
}
"""
schools_data = {"J": 8,
                "y": [28,  8, -3,  7, -1,  1, 18, 12],
                "sigma": [15, 10, 16, 11,  9, 11, 10, 18]}
posterior = stan.build(schools_code, data=schools_data)
fit = posterior.sample(num_chains=4, num_samples=1000)
eta = fit["eta"]  # array with shape (8, 4000)
df = fit.to_frame()  # pandas `DataFrame`

We appreciate citations as they let us discover what people have been doing with the software. Citations also provide evidence of use which can help in obtaining grant funding.

To cite PyStan in publications use:

Riddell, A., Hartikainen, A., & Carter, M. (2021). PyStan (3.0.0). https://pypi.org/project/pystan

Or use the following BibTeX entry:

@misc{pystan,
  title = {pystan (3.0.0)},
  author = {Riddell, Allen and Hartikainen, Ari and Carter, Matthew},
  year = {2021},
  month = mar,
  howpublished = {PyPI}
}

Please also cite Stan.