# Inconsistent results using Bayesian Model Averaging for model selection?

I have attempted to use Bayesian Model Averaging (BMA) as method to give guidance in the decision to include/omit factors in the linear factor stock return model:

$$r^i = X \beta^{i} + \epsilon^{i} \;\;\mathrm{for} \; i = 1,2,...,m$$

where $r^i$ is a (T x 1) vector, $X$ is an (N x k) matrix, $\beta^{i}$ is a (k x 1) vector, and $\epsilon^{i}$ is $N(0, \sigma_{i}^{2})$

I assumed a g-prior for $\beta^{i}$ and a diffuse prior for $\sigma_{i}^{2}$. After deriving the posterior probability of each model, I get the highest-probability model (i.e. the set of best predictors).

I then move on to testing these selected predictors using the Cross-Sectional Approach, also known as Fama-MacBeth procedure. This test reveals whether the selected predictors have a significant premium or not.

The odd thing is that only one of the BMA selected predictors has a statistically significant premium.

I am confused as to how to reconcile the results of BMA and Fama-MacBeth.

Any help would be greatly appreciated. Thanks!