The BGLIMM Procedure

Prior for the Scale Parameter

In models that have a scale parameter (see Table 13), you can specify the following prior distribution:

  • Inverse gamma distribution: pi left-parenthesis phi right-parenthesis equals IG left-parenthesis a comma b right-parenthesis. You can specify this distribution as follows:

    model y = x / scaleprior = igamma(shape=a, scale=b);
    

    The inverse gamma prior applies to all distributions that have a scale parameter.

  • Gamma distribution: pi left-parenthesis phi right-parenthesis equals gamma left-parenthesis a comma b right-parenthesis. You can specify this distribution as follows:

    model y = x / scaleprior = gamma(shape=a, iscale=b);
    

    The gamma prior applies to the gamma, inverse gamma, and negative binomial distributions. It does not apply to the normal likelihood function with an identity link.

  • Improper prior: pi left-parenthesis phi right-parenthesis proportional-to 1 slash phi. You can specify this distribution as follows:

    model y = x / scaleprior = improper;
    

    The improper prior applies to the gamma, inverse gamma, and negative binomial distributions. It does not apply to the normal likelihood function with an identity link.

Last updated: December 09, 2022