This is a model for NZ road deaths per billion km travelled, using data complied by Sam Warburton (@economissive on Twitter)
The model has an underlying smoothed trend which is a random walk with Gaussian increments, and a year-specific deviation that is also Gaussian. That is, it's a state space model with a random walk in the latent variable and a measurement model that's a Poisson-logNormal mixture to get overdispersed counts.
The variances of the random walk steps and the year-specific deviations have diffuse hyperpriors
and the means are set up so that the mean of the exponential of the increment is 1 -- ie, so
mu is genuinely the trend