The MCMC Procedure


PRIOR parameter-list distribution ;
HYPERPRIOR parameter-list distribution ;
HYPER parameter-list distribution ;

The PRIOR statement specifies the prior distribution of the model parameters. You must specify a single parameter or a list of parameters, a tilde , and then a distribution with its parameters. Multiple PRIOR statements are allowed for defining models with multiple independent prior components. The log of the prior is the sum of the log prior values from each of the PRIOR statements. See the section MODEL Statement for the names of the standard distributions and the section Standard Distributions for density specification.

The PRIOR statements are processed twice at every Markov chain simulation—that is, twice per pass through the data set. The statements are called at the first and the last observation of the data set. This is the same as how the BEGINNODATA and ENDNODATA statements are processed.

The HYPERPRIOR statement is internally treated the same as the PRIOR statement. It provides a notational convenience in case you want to fit a multilevel hierarchical model. It is used to specify the hyperprior distribution of the prior distribution parameters. The log of the hyperprior is the sum of the log hyperprior values from each of the HYPERPRIOR statements.

If you want to specify a multilevel hierarchical model, you can use either a PRIOR or a HYPERPRIOR statement as if it were a hyper-HYPERPRIOR statement. Your model can have as many hierarchical levels as desired.