Introduction to stan

Nowcasting and forecasting of infectious disease dynamics 
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What is stan and why do we use it?

  • a Probabilistic Programming Language for Bayesian inference (i.e., a way to write down models)

  • models are written in a text file (often ending .stan) and then loaded into an R/python/etc interface

  • once a model is written down, stan can be used to generate samples from the posterior distribution (using a variety of methods)

How to write a model in stan

In a stan model file we specify:

  • Data
    (types and names)

  • Parameters
    (types and names)

  • Model
    (prior and likelihood)


data {

}

parameters {

}

model {

}

Example: fairness of a coin

Data:

  • \(N\) coin flips

  • \(x\) times heads

Parameters

  • \(\theta\), probability of getting heads; uniform prior in \([0, 1]\)


{stan coin_model, output.var = "coin", eval = FALSE, echo = TRUE, file = nfidd::nfidd_cmdstan_model("coin")

Using stan from R

There are two packages for using stan from R. We will use the cmdstanr package:

library("cmdstanr")
mod <- nfidd::nfidd_cmdstan_model("coin")
mod
data {
  int<lower = 1> N;  // integer, minimum 1
  int<lower = 0> x; // integer, minimum 0
}

parameters {
  real<lower = 0, upper = 1> theta; // real, between 0 and 1
}

model {
  // Uniform prior
  theta ~ uniform(0, 1);
  // Binomial likelihood
  x ~ binomial(N, theta);
}

Sampling from the posterior

data <- list(
  N = 10, ## 10 coin flips
  x = 6 ## 6 times heads
)
mod$sample(data = data)
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 variable  mean median   sd  mad     q5   q95 rhat ess_bulk ess_tail
    lp__  -8.67  -8.40 0.74 0.33 -10.15 -8.15 1.00     1894     2058
    theta  0.58   0.58 0.14 0.15   0.35  0.80 1.00     1623     1774

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Introduction to stan