SMC Procedure
PRIOR Statement
PRIOR parameter-list ~ distribution ;
The PRIOR statement specifies the prior distribution and range of the model parameters. You must specify a single parameter or a list of parameters, a tilde (~), and then a distribution with its hyperparameters. Multiple PRIOR statements are permitted. The PRIOR statement is ignored if you specify the SUBMITMODEL statement.
With respect to each PRIOR statement, the syntax must have the following components in the order shown:
List of parameters: A list of parameters that have the same prior distribution.
Tilde: A tilde (~) symbol between the list of parameters and the distribution.
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Distribution with hyperparameters: A distribution that is specified in the form distribution-name(distribution-arguments). The available distribution-name and distribution-arguments in the prior statements are displayed in Table 5.
Table 5: Distribution Names and Arguments
Distribution Name Distribution Arguments Definitions BETA a, b Beta distribution with arguments shape parameter a and shape parameter b CAUCHY l, s Cauchy distribution with arguments location l and scale s GAMMA a, b Gamma distribution with arguments shape a and scale b IGAMMA a, b Inverse gamma distribution with arguments shape a and scale b LOGN m, s Log-normal distribution with arguments mean m and standard deviation s NORMAL | N m, s Normal distribution with arguments mean m and standard deviation s T m, s, 
Student’s —t distribution with arguments mean m, standard deviation s, and degrees of freedom
UNIFORM l, u Uniform distribution with arguments min l and scale u
The distribution-arguments are specified by numbers that are enclosed in parentheses and separated by commas.
The constant hyperparameters of a prior distribution are specified by constant numbers in parentheses. For example, the following statements specify the prior distributions of phi, var_1, and var_2, where the latter two parameters have the same prior distribution:
prior phi ~ uniform(-1, 1);
prior var_1 var_2 ~ igamma(0.01, 0.01);
The range of each model parameter defines its upper and lower bounds when you draw them from the random walk proposal in the PMCMC method. If any model parameter is not specified in any PRIOR statement, then the contribution of that parameter to the logarithmic prior density function, 
, is zero (see the section Particle Marginal Metropolis-Hastings Sampler), and the range of that parameter is defined by LOWER and UPPER options in the PARAMETERS statement (see the section PARAMETERS Statement). For any model parameter that you specify in the PRIOR statement, its range is defined by the intersection of the range specified in the PARAMETERS statement and the default range of the prior distribution. In addition, the range of that parameter defined in the PARAMETERS statement must be a subset of the default range of its prior distribution. For example, the following statements cause an error because 
:
parameter phi = 0.5 / lower = 0 upper = 1;
prior phi ~ uniform(0.2, 1);