Bayesian model of COVID-19 cases in U.S. counties.

The data is from the COVID-19 Event Risk Planner, which combines data from several sources including the NYTimes COVID19 data project and U.S. Census. It includes U.S. county-level COVID-19 data such as number of cases, deaths, and population.

I fit a hierarchical binomial model for the counts of COVID-19 cases in each U.S. county. The model treats each county as population members and uses partial pooling to estimate county-level COVID-19 cases. Partial pooling means the county-level COVID-19 probabilities are modeled by a distribution. This allows for information sharing among these parameters.

The Stan model is below:

data {
  int<lower=0> N;     // counties
  int<lower=0> y[N];  // cases
  int<lower=0> K[N];  // populations
}
parameters {
  real<lower=0, upper=1> phi;  // population chance of covid
  real<lower=1> kappa;         // population concentration
  vector<lower=0, upper=1>[N] theta;  // chance of covid
}
model {
  kappa ~ pareto(1, 1.5);  // hyperprior
  theta ~ beta(phi * kappa, (1 - phi) * kappa); // prior
  y ~ binomial(K, theta); // likelihood
}