I have a dataset with three variables, where all variables are quantitatives. Let call it $y$, $x_1$ and $x_2$. I'm fitting a regression model in a Bayesian perspective via MCMC with rjags

I done a exploratory analysis and the scatterplot of $y\times x_2$ suggest that a quadratic term should be used. Then I fitted two models

(1) $y=\beta_0+\beta_1*x_1+\beta_2*x_2$

(2) $y=\beta_0+\beta_1*x1+\beta_2*x_2+\beta_3*x_1x_2+\beta_4*x_1^2+\beta_5*x_2^2$

In model 1 the effect size of each parameter is not small and the 95% credible interval not contains the value $0$.

In model 2 the effect size of parameters $\beta_3$ and $\beta_4$ are small and each of credible intervals for all parameters contains $0$.

The fact that a credible interval contains $0$ is enough to say that the parameter is not significant?

Then I adjusted the following model

(3)$y=\beta_0+\beta_1*x_1+\beta_2*x_2+\beta_3*x^2_2$

The effect size of each parameter is not small, but with exception of $\beta_1$ all credible intervals contains $0$.

Which is the right way to do variable selection in Bayesian statistics?

**EDIT:**Below is a example of a parameter which credible interval contains the value 0.

In this case is reasonable say that $\beta_4\neq 0$?