Bayesian One-way 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
Normal-Inverse-Gamma 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 a0 for Inverse-Gamma distribution. You must enter a single value that is greater than 0.
- Scale Parameter
- Specify the scale parameter b0 for Inverse-Gamma 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 β0 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: σ2x
- Specify V0 the values in the lower triangle in the variance-covariance matrix
for the multivariate normal prior. Note that V0 must be semi-positive 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 off-diagonal values are 0.
Click Reset to clear the values.
- Use identity matrix
- When selected, the identity matrix is used. You cannot specify V0 values in the lower triangle in the variance-covariance matrix for the multivariate normal prior.