Bayesian modelling is flexible, but I’ve found that there are surprisingly few template models out there for even basic models like Poisson and negative binomial. The ones that exist are usually buried in a whole article that you have to pick through. So here are two simple examples used for count data, for reference:
###Poisson:
model
{
# Weakly informative priors
beta0 ~ dnorm(0, 1)
beta1 ~ dnorm(0, 1)
# N is the sample size
for(i in 1:N)
{
# Y is the response variable (as a count)
Y[i] ~ dpois(lambda[i])
# X is the exposure variable, and offset.variable is the offset for Y
# Using a log-link function for the count data
log(lambda[i]) <- beta0 +
beta1 * X[i] +
log(offset.variable[i])
}
}Negative binomial:
model
{
# Weakly informative priors
beta0 ~ dnorm(0, 1)
beta1 ~ dnorm(0, 1)
r ~ dunif(0, 50)
# N is the sample size
for(i in 1:N)
{
# Y is the response variable (as a count)
Y[i] ~ dnegbin(p[i], r)
# X is the exposure variable, and offset.variable is the offset for Y
# Using a log-link function for the count data
log(mu[i]) <- beta0 +
beta1 * X[i] +
log(offset.variable[i])
# Transforms mu into p, which is used by the negative binomial distribution
p[i] <- r/(r + mu[i])
}
}