1 What is Stan?

By the end of this section, you’ll understand that Stan is a probabilistic programming language for specifying statistical models, an open-source community, as well as a broader software ecosystem.

1.1 Language, Community, Ecosystem

Stan is …

an open-source community consisting of people from a variety of different backgrounds (Cognitive Science, Computer Science, Statistics, etc.).
an open-source ecosystem consisting of a core library, interfaces for multiple programming languages, and a growing collection of contributed packages.
a probabilistic programming language for specifying statistical models.

1.1.1 An open-source community

We communicate via:

Slack
- different channels (e.g., #general, #help)
- mainly developer discussions
Discourse
- questions, discussion, and announcements related to Stan
- for both users and developers
GitHub
- code repositories
- issue tracker for reporting bugs and requesting features
- pull requests for contributing code, documentation, examples, etc.
Stan Website
- documentation, tutorials, case studies, etc.

1.1.2 An open-source ecosystem

Multiple packages/libraries that work together to provide a complete probabilistic programming environment

1.1.3 A probabilistic programming language

A probabilistic programming language for specifying statistical models.

data {
  int N;   // number of observations
  int J;   // number of students
  int K;   // number of items on exam
  array[N] int<lower=0, upper=J> student;
  array[N] int<lower=0, upper=K> item;
  array[N] int<lower=0, upper=1> y;
  vector[J] x;
  real mu_mu_a, mu_mu_b;
  real<lower=0> sigma_mu_a, sigma_mu_b, mu_sigma_a, mu_sigma_b;
}
transformed data {
  vector[J] x_adj = (x - mean(x))/sd(x);
}
parameters {
  real mu_a, mu_b;
  real<lower=0> sigma_a, sigma_b;
  vector<offset=mu_a, multiplier=sigma_a>[K] a;
  vector<offset=mu_b, multiplier=sigma_b>[K] b;
}
model {
  a ~ normal(mu_a, sigma_a);
  b ~ normal(mu_b, sigma_b);
  mu_a ~ normal(mu_mu_a, sigma_mu_a);
  mu_b ~ normal(mu_mu_b, sigma_mu_b);
  sigma_a ~ exponential(1/mu_sigma_a);
  sigma_b ~ exponential(1/mu_sigma_b);
  y ~ bernoulli(0.25 + 0.75*inv_logit(a[item] + b[item] .* x_adj[student]));
}