Installing and running Stan

Outline

Topics

• What is Stan?
• Links to install.

Rationale

SNIS and simPPLe are very flexible and relatively easy to understand, but it can be very slow.

Stan is an alternative way to approximate posterior distributions, with complementary properties:

	SNIS	Stan
Speed	Slow	Faster1
Flexibility	Very flexible	Less flexible2
Easy to understand?	Simple	More complex3

From a pedagogical point of view, it is useful to first learn about SNIS, however for real-world models, one would typically use Stan, or some other advanced inference method, due to the poor scalability of SNIS.

What is Stan?

• Stan is the most popular PPL as of 2024.
• Review the notes on “what is a PPL.”
• Stan uses Markov chain Monte Carlo (MCMC) to approximate the posterior distribution.
  • Think of MCMC as a drop-in replacement for SNIS.
  • We will talk about it in more detail soon.

Installing Stan

You will need Stan installed to complete the exercises and clicker questions after the quiz. Don’t wait until the last minute, install it today!

There are two main steps to install Stan:

1. Configuring a C++ Toolchain
2. Installing RStan

Let us know on Piazza if you encounter any issues!

Running Stan

We present two methods for running Stan in the next two sections: either from an R script, or from a notebook.

Template: to quickly get started, download the following templates which you can use as a starting point for either R script or notebook.

From a R script

First, copy and paste the following code into a file called beta_binomial.stan:

beta_binomial.stan

data {
  int<lower=0> n;         // number of trials
  int<lower=0,upper=n> k; // number of successes
}

parameters {
  real<lower=0,upper=1> p;
}

model {
  // prior
  p ~ beta(1,1);

  // likelihood
  k ~ binomial(n, p);
}

Second, run Stan as follows:

require(rstan)

fit = stan(
  seed = 123,
  file = "beta_binomial.stan",  # Stan program
  data = list(n=3, k=3),        # named list of data
  iter = 1000                   # number of samples to draw
)

The first question of the next exercise will be to report the posterior median, which can be obtained under the column “50%” of the output of the following R command:

print(fit)

From a notebook

To see an example of how to integrate Stan code inside quarto (R markdown would work the same), see the source code used for the next page in the notes, available on github.

Footnotes

1. Often MCMC algorithms such as stan scale polynomially in dimension while SNIS scales exponentially.

2. For example, Stan does not support latent integer-value random variables, whereas simPPLe does.

3. simPPLe is a few dozen lines of code, whereas Stan has millions of lines of code.