How to obtain the variable importance in bayesian hierarchical model

I am establishing a Bayesian hierarchical model. Statistical significance of coefficients is less important in Bayesian statistics compared to frequentist statistics. Consequently, I am interested in how to determine variable importance in a Bayesian hierarchical model. However, I cannot find any guidance on this topic. Any help would be greatly appreciated.

I found your question a little hard to understand. Do you mean variable importance in the interpretable machine learning sense, or something else?

i read the BDA again and think analysis of variance is a solution.