Below is some OpenBUGS code that I created that models income as a function of age, race, and educational status. This is a simple MR example and can easily be replicated in R with the lm() function.
## OpenBUGS Model
model{
for( i in 1:6641) {
income[i] ~ dnorm(mu[i], tau)
mu[i] <- beta0 + beta1*educ[i] + beta2*age[i] + beta3*race[i]
}
## Priors
#beta0 ~ dflat()
#beta1 ~ dflat()
#beta2 ~ dflat()
#beta3 ~ dflat()
## Hypothesized Priors, deduced by "peaking"
beta0 ~ dnorm(3, 0.1)
beta1 ~ dnorm(0.3, 0.1)
beta2 ~ dnorm(0.01,0.5)
beta3 ~ dnorm(0, 0.1)
tau ~ dgamma(0.1,0.1)
sigma <- 1/sqrt(tau)
}
## Initial values
list(beta0 = 0, beta1 = 1, beta2 = 1, beta3 = 1, tau = 1)
You can get the data and a file that contains the model and the initial values here. This is example is entirely didactic, comes with no warranty, and is entirely intended to help get folks up and running in *BUGS.
The most interesting bits: With this large sample size (n ~ 6000), the priors seem to be washed away by the data and the high similarity between the results from the Bayesian and the frequentist analyses (run via lm in R).
