Figure 2.

Directed Acyclic Graph for BMA and its parameters. Boxes represent observed quantities, ovals parameters to be updated over the course of MCMC, and rounded boxes fixed meta-parameters. Y denotes the dependent variable, and ν indexes the sets X of independent predictor variables and β of corresponding estimates. I indicates inclusion of the νth variable and is Bernoulli-distributed with parameter p_ν, which, in turn, follows a beta distribution with parameters (a_t, b_t) depending on the interaction level t of the variable. The variance of the coefficients β_ν is modeled by a residual variance term σ² following a half-Cauchy prior, and a variance inflation factor ψ_t depending on the interaction level and following a log-normal distribution with mean μ_t and variance τ_t.