CQLIM Procedure

PRIOR Statement

PRIOR parameter-list ~ distribution ;

The PRIOR statement specifies the prior distribution of the model parameters for Bayesian analysis. You must specify a single parameter or a list of parameters, a tilde (~), and then a distribution with its parameters. You can specify multiple PRIOR statements, although PRIOR statements for parameters that do not exist in the model are ignored. For information about how parameters are named so that you can refer to them when specifying prior distributions, see the section Naming of Parameters. Alternatively, specifying the SHOWNAMES suboption of the PRIORSUMMARY option in the BAYES statement displays the names that are used for all parameters in the prior summary table.

You can specify the following distributions. All hyperparameters of the distribution must be specified, except LOWER and UPPER, which determine the support of the distribution and allow for truncated versions of many of them. For more information about these distributions, see the section Standard Prior Distributions in Chapter 2, Introduction to Bayesian Analysis Procedures. For more information about truncated prior distributions, see the section Truncated Prior Distributions.

CAUCHY(cauchy-options)

specifies independently and identically distributed Cauchy distributions for the parameter-list.

You must specify the following cauchy-options:

LOCATION= LOC=: specifies the location parameter of the Cauchy distribution.
SCALE=: specifies the scale parameter of the Cauchy distribution, where .

You can also specify the following cauchy-options:

LOWER=L | NEGATIVEINFINITY LB=L | NEGATIVEINFINITY

specifies the lower bound of the Cauchy distribution, where . You can specify the following values:

L: uses L as the lower bound, such that the prior becomes a truncated Cauchy distribution.
NEGATIVEINFINITY NEGINFTY NEGINF: uses negative infinity as the lower bound.

By default, LOWER=NEGATIVEINFINITY.

UPPER=U | INFINITY UB=U | INFINITY

specifies the upper bound of the Cauchy distribution, where . You can specify the following values:

U: uses U as the upper bound, such that the prior becomes a truncated Cauchy distribution.
INFINITY INFTY INF: uses positive infinity as the upper bound.

By default, UPPER=INFINITY.

GAMMA(gamma-options)

specifies independently and identically distributed gamma distributions for the parameter-list. You must specify the following gamma-options:

SCALE=b: specifies the scale parameter of the gamma distribution, where .
SHAPE=a: specifies the shape parameter of the gamma distribution, where .

You can also specify the following gamma-options:

LOWER=L LB=L

specifies the lower bound of the gamma distribution, where and . If , the prior becomes a truncated gamma distribution.

By default, LOWER=0.

UPPER=U | INFINITY UB=U | INFINITY

specifies the upper bound of the gamma distribution, where . You can specify the following values:

U: uses U as the upper bound, such that the prior becomes a truncated gamma distribution.
INFINITY INFTY INF: uses positive infinity as the upper bound.

By default, UPPER=INFINITY.

IGAMMA(igamma-options)

specifies independently and identically distributed inverse gamma distributions for the parameter-list. You must specify the following igamma-options:

SCALE=b: specifies the scale parameter of the inverse gamma distribution, where .
SHAPE=a: specifies the shape parameter of the inverse gamma distribution, where .

You can also specify the following igamma-options:

LOWER=L LB=L

specifies the lower bound of the inverse gamma distribution, where and . If , the prior becomes a truncated inverse gamma distribution.

By default, LOWER=0.

UPPER=U | INFINITY UB=U | INFINITY

specifies the upper bound of the inverse gamma distribution, where . You can specify the following values:

U: uses U as the upper bound, such that the prior becomes a truncated inverse gamma distribution.
INFINITY INFTY INF: uses positive infinity as the upper bound.

By default, UPPER=INFINITY.

NORMAL(normal-options)

specifies independently and identically distributed normal distributions for the parameter-list. You must specify the MEAN= normal-option and either the SD= or VAR= normal-option:

MEAN=: specifies the mean parameter of the normal distribution.
SD=: specifies the standard deviation parameter of the normal distribution, where .
VAR=: specifies the variance parameter of the normal distribution, where .

You can also specify the following normal-options:

LOWER=L | NEGATIVEINFINITY LB=L | NEGATIVEINFINITY

specifies the lower bound of the normal distribution, where . You can specify the following values:

L: uses L as the lower bound, such that the prior becomes a truncated normal distribution.
NEGATIVEINFINITY NEGINFTY NEGINF: uses negative infinity as the lower bound.

By default, LOWER=NEGATIVEINFINITY.

UPPER=U | INFINITY UB=U | INFINITY

specifies the upper bound of the normal distribution, where . You can specify the following values:

U: uses U as the upper bound, such that the prior becomes a truncated normal distribution.
INFINITY INFTY INF: uses positive infinity as the upper bound.

By default, UPPER=INFINITY.

SQRTGAMMA(sqrtgamma-options)

specifies independently and identically distributed square root gamma distributions for the parameter-list. You must specify the following sqrtgamma-options:

SCALE=b: specifies the scale parameter of the square root gamma distribution, where .
SHAPE=a: specifies the shape parameter of the square root gamma distribution, where .

You can also specify the following sqrtgamma-options:

LOWER=L LB=L

specifies the lower bound of the square root gamma distribution, where and . If , the prior becomes a truncated square root gamma distribution.

By default, LOWER=0.

UPPER=U | INFINITY UB=U | INFINITY

specifies the upper bound of the square root gamma distribution, where . You can specify the following values:

U: uses U as the upper bound, such that the prior becomes a truncated square root gamma distribution.
INFINITY INFTY INF: uses positive infinity as the upper bound.

By default, UPPER=INFINITY.

SQRTIGAMMA(sqrtigamma-options)

specifies independently and identically distributed square root inverse gamma distributions for the parameter-list. You must specify the following sqrtigamma-options:

SCALE=b: specifies the scale parameter of the square root inverse gamma distribution, where .
SHAPE=a: specifies the shape parameter of the square root inverse gamma distribution, where .

You can also specify the following sqrtigamma-options:

LOWER=L LB=L

specifies the lower bound of the square root inverse gamma distribution, where and . If , the prior becomes a truncated square root inverse gamma distribution.

By default, LOWER=0.

UPPER=U | INFINITY UB=U | INFINITY

specifies the upper bound of the square root inverse gamma distribution, where . You can specify the following values:

U: uses U as the upper bound, such that the prior becomes a truncated square root inverse gamma distribution.
INFINITY INFTY INF: uses positive infinity as the upper bound.

By default, UPPER=INFINITY.

T(t-options)

specifies independently and identically distributed t distributions for the parameter-list.

You must specify the following t-options:

DF=: specifies the degrees-of-freedom parameter of the t distribution, where .
LOCATION= LOC=: specifies the location parameter of the t distribution.
SCALE=: specifies the scale parameter of the t distribution, where .

You can also specify the following t-options:

LOWER=L | NEGATIVEINFINITY LB=L | NEGATIVEINFINITY

specifies the lower bound of the t distribution, where . You can specify the following values:

L: uses L as the lower bound, such that the prior becomes a truncated t distribution.
NEGATIVEINFINITY NEGINFTY NEGINF: uses negative infinity as the lower bound.

By default, LOWER=NEGATIVEINFINITY.

UPPER=U | INFINITY UB=U | INFINITY

specifies the upper bound of the t distribution, where . You can specify the following values:

U: uses U as the upper bound, such that the prior becomes a truncated t distribution.
INFINITY INFTY INF: uses positive infinity as the upper bound.

By default, UPPER=INFINITY.

UNIFORM(uniform-options)

specifies independently and identically distributed uniform distributions for the parameter-list. You must specify both the following uniform-options:

MAX=M | INFINITY

specifies the maximum value of the uniform distribution, where . You can specify the following values:

M: uses M as the maximum value.
INFINITY INFTY INF: uses positive infinity as the maximum value, such that the prior becomes an improper uniform prior.

MIN=m | NEGATIVEINFINITY

specifies the minimum value of the uniform distribution, where . You can specify the following values:

m: uses m as the minimum value.
NEGATIVEINFINITY NEGINFTY NEGINF: uses negative infinity as the minimum value, such that the prior becomes an improper uniform prior.

Last updated: July 09, 2026