In greta: Simple and Scalable Statistical Modelling in R

Air

Air analyses reported respiratory illness versus exposure to nitrogen dioxide in 103 children. The parameters alpha, beta and sigma2 are known in advance, and the data are grouped into three categories.

See WinBUGS examples volume 2 (pdf) for details.

data

y <- c(21, 20, 15)
n <- c(48, 34, 21)
Z <- c(10, 30, 50)
alpha <- 4.48
beta <- 0.76
sigma2 <- 81.14
sigma <- sqrt(sigma2)
tau <- 1 / sigma2
J <- 3

greta code

theta <- normal(0, 32, dim = 2)
mu <- alpha + beta * Z
X <- normal(mu, sigma)
p <- ilogit(theta[1] + theta[2] * X)
distribution(y) <- binomial(n, p)

BUGS/JAGS code

for(j in 1 : J) {
   y[j] ~ dbin(p[j], n[j])
   logit(p[j]) <- theta[1] + theta[2] * X[j]
   X[j] ~ dnorm(mu[j], tau)
   mu[j] <- alpha + beta * Z[j]
}
theta[1] ~ dnorm(0.0, 0.001)
theta[2] ~ dnorm(0.0, 0.001)

Stan code

cat(readLines('https://raw.githubusercontent.com/stan-dev/example-models/master/bugs_examples/vol2/air/air.stan'), sep = '\n')

greta documentation built on Sept. 8, 2022, 5:10 p.m.