In my research, I am utilizing the Bayesian Model Averaging (BMA) methodology to identify the best set of regressors that can predict the outcome variable $y$. My dataset consists of five variables and forty-three observations. I am performing all the calculations in R using the BMA package.
I am in a peculiar situation. The given regressor has a high posterior inclusion probability of 0.89, but its corresponding sigma is twice the estimated beta parameter. The frequentist confidence interval includes zero, which leads to the conclusion that the evidence does not support the hypothesis that the beta parameter differs from zero.
It is possible that the alleged contradiction can be explained by the heterogeneity of the effects. The beta parameter's corresponding kernel estimate shows a significant dispersion of values and marked skewness, which makes the variable relevant, but its effect unclear. This type of reasoning follows a Bayesian conceptual scheme.
Does the Bayesian interpretation make sense in my context?
