# PyStan¶

Release v3.9.0

**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

Open source software: ISC License

(Upgrading from PyStan 2? We have you covered: Upgrading to Newer Releases.)

## Quick start¶

Install PyStan with `python3 -m 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.

This block of code shows how to use PyStan with a hierarchical model used to study coaching effects across eight schools (see Section 5.5 of Gelman et al. (2003)).

```
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, requires pandas
```