20241209-Vaccine

data.json

{
  "a0": 0.700102,
  "b0": 1.0,
  "n": 94,
  "y": 8
}

main.stan

data { // everything to the right of the | in Bayes' Rule
  real<lower = 0> a0; // expectation for normal prior on VE
  real<lower = 0> b0; // standard deviation for normal prior on VE
  int<lower = 0>  n; // number of people with Covid in the RCT
  int<lower = 0, upper = n> y; // number of them who were vaccinated
}
parameters { // everything to the left of the | in Bayes' Rule
  real<upper = 1> theta; // = 1 - Pr(covid | vax) / Pr(covid | placebo)
}
model { // target has been initialized to zero basically
  target += beta_lpdf(theta | a0, b0);      // prior log-kernel
  target += binomial_lpmf(y | n, theta); // log-likelihood
} // model block is like a function that returns target
generated quantities { 
  real<lower = 0, upper = 1> VE = (1 - 2 * theta) / (1 - theta);
}

meta.json

{"title":"Untitled"}

sampling_opts.json

{"num_chains":4,"num_warmup":1000,"num_samples":1000,"init_radius":2}