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
}
