PRIOR Subcommand (BAYES ONESAMPLE: Poisson command)
PRIOR specifies the prior distribution.
VARDIST. Specify the prior distribution for the variance parameter. Valid when neither
the data variance nor PRECDIST is specified. The diffuse prior is the default
setting. When the data variance is specified for some variables, VARDIST is
ignored for those variables.
- DIFFUSE: Specify the diffuse prior ∝ 1.
- INVCHISQ(value1 value2): Specify the distribution and parameters for inverse -χ2(ν0,σ20), where ν0 > 0 is the degree of freedom, and σ20 > 0 is the scale parameter.
- INVGAMMA(value1 value2): Specify the distribution and parameters for inverse-Gamma(α0,β0),where α0 > 0 is the shape parameter, and β0 > 0 is the scale parameter.
PREDIST. Specify the prior distribution for the precision parameter. The parameter is
valid when neither the data variance nor VARDIST are specified. The subcommand is
an mutually exclusive to VARDIST.
- GAMMA(value1 value2): Specify the distribution and parameters for Gamma(α0,β0), where α0 > 0 is the shape parameter, and β0 is the scale parameter.
- CHISQ(value): Specify the distribution and parameters for χ2(ν0), where ν0 > 0 is the degree of freedom.
TYPE. Specify the conjugate prior for Poisson parameters for characterizing posterior distribution. For Poisson, the conjugate prior follows a Gamma distribution. For Poisson-Gamma relationship, the support range is value1 > 0 and value2 ≥ 0 to accommodate the Uniform and the Jeffreys priors. The parameter is valid only when DISTRIBUTION = POISSON.