Consider a generic model for simple linear regression. The data are metric values, modeled as coming from a normal distribution that has mean parameter μ=β0+β1x1 and precision parameter τ (=1/σ2). The priors on the intercept and slope parameters (β0 and β1) are normal, and the prior on the precision is gamma.
Notice that the description of the model started with the nature of the data, then described the likelihood function, then described the prior. This is the sequential order of description that makes sense for communicating to people. First you have to know the nature of the data being modeled. Next, you have to know the choice of likelihood function. For example, the metric data might have been modeled by a normal distribution, or by a log-normal distribution, or by a Weibull distribution, or by a t distribution, or whatever. Each of those likelihood functions has different parameters. Once the likelihood function is specified, with its corresponding parameters, then it makes sense to talk about the prior on those parameters.
The JAGS/BUGS code, in all the book's programs, specifies the model details in that order: from data, to likelihood, to prior. For example, here is the model specification for simple linear regression:
Therefore, the hierarchical diagrams should always be read starting at the bottom, then working upward.