Bayesian Oneway ANOVA: Priors
You can specify the following prior distribution settings for the regression parameters and the variance of the errors. The following options are available only when the Characterize Posterior Distribution option is selected for Bayesian Analysis.
Note: Many applied researchers may question the need to specify a prior. Reference priors
minimize the concern where the prior is generally overwhelmed as the data increases. When
informative prior information is specified, Bayesian methods can effectively use the information.
The requirement to specify a prior should not be viewed as a deterrent to using Bayesian
analysis.
 Reference
 When selected, reference analysis produces objective Bayesian inference. Inferential statements depend only on the assumed model and the available data, and the prior distribution that is used to make an inference is the least informative. This is the default setting.
 Conjugate
 Provides options for defining conjugate prior distributions. Conjugate priors assume the
NormalInverseGamma joint distribution. Although conjugate priors are not required when performing
Bayesian updates, they aid the calculation processes.
 Priors on variance of errors

 Shape Parameter
 Specify the shape parameter a_{0} for InverseGamma distribution. You must enter a single value that is greater than 0.
 Scale Parameter
 Specify the scale parameter b_{0} for InverseGamma distribution. You must enter a single value that is greater than 0. The larger the scale parameter, the more spread out the distribution.
 Priors on regression parameters
 Specify the mean vector β_{0} for the group means. The number of values must meet
the number of regression parameters, including the intercept term.
The Variables column is automatically populated with the levels of the Factor. The Mean column does not include any default values.
Click Reset to clear the values.
 Variance of covariance matrix: σ^{2}x
 Specify V_{0} the values in the lower triangle in the variancecovariance matrix
for the multivariate normal prior. Note that V_{0} must be semipositive definite.
Only the lower triangle of the table must be specified.
The rows and columns are automatically populated with the levels of the Factor. All of the diagonal values are 1; all of the offdiagonal values are 0.
Click Reset to clear the values.
 Use identity matrix
 When selected, the identity matrix is used. You cannot specify V_{0} values in the lower triangle in the variancecovariance matrix for the multivariate normal prior.